On the convergence of an algorithm constructing the normal form for elliptic lower dimensional tori in planetary systems View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2014-08

AUTHORS

Antonio Giorgilli, Ugo Locatelli, Marco Sansottera

ABSTRACT

We give a constructive proof of the existence of elliptic lower dimensional tori in nearly integrable Hamiltonian systems. In particular we adapt the classical Kolmogorov normalization algorithm to the case of planetary systems, for which elliptic tori may be used as replacements of elliptic Keplerian orbits in Lagrange-Laplace theory. With this paper we support with rigorous convergence estimates the semi-analytic work in our previous article (Sansottera et al., Celest Mech Dyn Astron 111:337–361, 2011), where an explicit calculation of an invariant torus for a planar model of the Sun-Jupiter-Saturn-Uranus system has been made. With respect to previous works on the same subject we exploit the characteristic of Lie series giving a precise control of all terms generated by our algorithm. This allows us to slightly relax the non-resonance conditions on the frequencies. More... »

PAGES

397-424

References to SciGraph publications

  • 1994-07. Twistless KAM tori in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1995-03. Superexponential stability of KAM tori in JOURNAL OF STATISTICAL PHYSICS
  • 2013-10. On the extension of the Laplace-Lagrange secular theory to order two in the masses for extrasolar systems in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1999. A Classical Self-Contained Proof of Kolmogorov’s Theorem on Invariant Tori in HAMILTONIAN SYSTEMS WITH THREE OR MORE DEGREES OF FREEDOM
  • 2000-09. Invariant Tori in the Secular Motions of the Three-body Planetary Systems in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1971-07. Existence of quasi-periodic solutions to the three-body problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2003-11. Elliptic Two-Dimensional Invariant Tori for the Planetary Three-Body Problem in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2009-06. Kolmogorov and Nekhoroshev theory for the problem of three bodies in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1997-01. Invariant KAM tori and global stability for Hamiltonian systems in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • 2011-11. A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2011-08. Branching of Cantor Manifolds of Elliptic Tori and Applications to PDEs in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2015-08. Improved convergence estimates for the Schröder–Siegel problem in ANNALI DI MATEMATICA PURA ED APPLICATA (1923 -)
  • 1989-12. On elliptic lower dimensional tori in hamiltonian systems in MATHEMATISCHE ZEITSCHRIFT
  • 1997-03. Kolmogorov theorem and classical perturbation theory in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10569-014-9562-7

    DOI

    http://dx.doi.org/10.1007/s10569-014-9562-7

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1035910283


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "University of Milan", 
              "id": "https://www.grid.ac/institutes/grid.4708.b", 
              "name": [
                "Dipartimento di Matematica, Universit\u00e0 degli Studi di Milano, via Saldini 50, 20133, Milano, Italy"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Giorgilli", 
            "givenName": "Antonio", 
            "id": "sg:person.010532704656.30", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010532704656.30"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Rome Tor Vergata", 
              "id": "https://www.grid.ac/institutes/grid.6530.0", 
              "name": [
                "Dipartimento di Matematica, Universit\u00e0 degli Studi di Roma \u201cTor Vergata\u201d, Via della Ricerca Scientifica 1, 00133, Roma, Italy"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Locatelli", 
            "givenName": "Ugo", 
            "id": "sg:person.07637253565.17", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07637253565.17"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Namur", 
              "id": "https://www.grid.ac/institutes/grid.6520.1", 
              "name": [
                "D\u00e9partement de Math\u00e9matique and NAXYS, Universit\u00e9 de Namur, Rempart de la Vierge 8, 5000, Namur, Belgium"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Sansottera", 
            "givenName": "Marco", 
            "id": "sg:person.012027575165.98", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012027575165.98"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf01227790", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001288867", 
              "https://doi.org/10.1007/bf01227790"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01227790", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001288867", 
              "https://doi.org/10.1007/bf01227790"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02180145", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004400049", 
              "https://doi.org/10.1007/bf02180145"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02180145", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004400049", 
              "https://doi.org/10.1007/bf02180145"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00205-003-0269-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008228544", 
              "https://doi.org/10.1007/s00205-003-0269-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1011139523256", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009130340", 
              "https://doi.org/10.1023/a:1011139523256"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-011-1264-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009792688", 
              "https://doi.org/10.1007/s00220-011-1264-3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10231-014-0408-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011031562", 
              "https://doi.org/10.1007/s10231-014-0408-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10231-014-0408-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011031562", 
              "https://doi.org/10.1007/s10231-014-0408-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01221590", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013571657", 
              "https://doi.org/10.1007/bf01221590"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01221590", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013571657", 
              "https://doi.org/10.1007/bf01221590"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10569-013-9501-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017966435", 
              "https://doi.org/10.1007/s10569-013-9501-z"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/pl00001462", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021394303", 
              "https://doi.org/10.1007/pl00001462"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10569-009-9192-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021916524", 
              "https://doi.org/10.1007/s10569-009-9192-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10569-009-9192-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021916524", 
              "https://doi.org/10.1007/s10569-009-9192-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10569-011-9375-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024463109", 
              "https://doi.org/10.1007/s10569-011-9375-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-94-011-4673-9_8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025219621", 
              "https://doi.org/10.1007/978-94-011-4673-9_8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.matcom.2010.11.018", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039296165"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/pl00001475", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042122109", 
              "https://doi.org/10.1007/pl00001475"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02108809", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046115209", 
              "https://doi.org/10.1007/bf02108809"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02108809", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046115209", 
              "https://doi.org/10.1007/bf02108809"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1070/rm1963v018n06abeh001143", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058193727"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1070/rm1977v032n06abeh003859", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058194264"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1070/sm1989v064n02abeh003316", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058200759"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1086/109964", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058448574"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/s0036141004443646", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062876034"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0129055x96000135", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062898633"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.3934/dcdsb.2007.7.377", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1071736148"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.3934/dcdss.2010.3.601", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1071737698"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.3934/dcdss.2010.3.601", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1071737698"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2014-08", 
        "datePublishedReg": "2014-08-01", 
        "description": "We give a constructive proof of the existence of elliptic lower dimensional tori in nearly integrable Hamiltonian systems. In particular we adapt the classical Kolmogorov normalization algorithm to the case of planetary systems, for which elliptic tori may be used as replacements of elliptic Keplerian orbits in Lagrange-Laplace theory. With this paper we support with rigorous convergence estimates the semi-analytic work in our previous article (Sansottera et al., Celest Mech Dyn Astron 111:337\u2013361, 2011), where an explicit calculation of an invariant torus for a planar model of the Sun-Jupiter-Saturn-Uranus system has been made. With respect to previous works on the same subject we exploit the characteristic of Lie series giving a precise control of all terms generated by our algorithm. This allows us to slightly relax the non-resonance conditions on the frequencies.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s10569-014-9562-7", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136436", 
            "issn": [
              "0008-8714", 
              "0923-2958"
            ], 
            "name": "Celestial Mechanics and Dynamical Astronomy", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "3-4", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "119"
          }
        ], 
        "name": "On the convergence of an algorithm constructing the normal form for elliptic lower dimensional tori in planetary systems", 
        "pagination": "397-424", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "ab10a9972e863fb11ea2987328c8472548a9c0b026192058bbdbf2f0f7c3a125"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s10569-014-9562-7"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1035910283"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s10569-014-9562-7", 
          "https://app.dimensions.ai/details/publication/pub.1035910283"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-10T19:57", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8681_00000514.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007%2Fs10569-014-9562-7"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s10569-014-9562-7'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s10569-014-9562-7'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10569-014-9562-7'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10569-014-9562-7'


     

    This table displays all metadata directly associated to this object as RDF triples.

    164 TRIPLES      21 PREDICATES      50 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s10569-014-9562-7 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N8ccbf169f20941e1bbcfe3bb41beadad
    4 schema:citation sg:pub.10.1007/978-94-011-4673-9_8
    5 sg:pub.10.1007/bf01221590
    6 sg:pub.10.1007/bf01227790
    7 sg:pub.10.1007/bf02108809
    8 sg:pub.10.1007/bf02180145
    9 sg:pub.10.1007/pl00001462
    10 sg:pub.10.1007/pl00001475
    11 sg:pub.10.1007/s00205-003-0269-2
    12 sg:pub.10.1007/s00220-011-1264-3
    13 sg:pub.10.1007/s10231-014-0408-4
    14 sg:pub.10.1007/s10569-009-9192-7
    15 sg:pub.10.1007/s10569-011-9375-x
    16 sg:pub.10.1007/s10569-013-9501-z
    17 sg:pub.10.1023/a:1011139523256
    18 https://doi.org/10.1016/j.matcom.2010.11.018
    19 https://doi.org/10.1070/rm1963v018n06abeh001143
    20 https://doi.org/10.1070/rm1977v032n06abeh003859
    21 https://doi.org/10.1070/sm1989v064n02abeh003316
    22 https://doi.org/10.1086/109964
    23 https://doi.org/10.1137/s0036141004443646
    24 https://doi.org/10.1142/s0129055x96000135
    25 https://doi.org/10.3934/dcdsb.2007.7.377
    26 https://doi.org/10.3934/dcdss.2010.3.601
    27 schema:datePublished 2014-08
    28 schema:datePublishedReg 2014-08-01
    29 schema:description We give a constructive proof of the existence of elliptic lower dimensional tori in nearly integrable Hamiltonian systems. In particular we adapt the classical Kolmogorov normalization algorithm to the case of planetary systems, for which elliptic tori may be used as replacements of elliptic Keplerian orbits in Lagrange-Laplace theory. With this paper we support with rigorous convergence estimates the semi-analytic work in our previous article (Sansottera et al., Celest Mech Dyn Astron 111:337–361, 2011), where an explicit calculation of an invariant torus for a planar model of the Sun-Jupiter-Saturn-Uranus system has been made. With respect to previous works on the same subject we exploit the characteristic of Lie series giving a precise control of all terms generated by our algorithm. This allows us to slightly relax the non-resonance conditions on the frequencies.
    30 schema:genre research_article
    31 schema:inLanguage en
    32 schema:isAccessibleForFree false
    33 schema:isPartOf N12b4993ff3c842bfa99cfdb0c29c09dc
    34 Ne264c7038cc04f1d84f57921f48d7add
    35 sg:journal.1136436
    36 schema:name On the convergence of an algorithm constructing the normal form for elliptic lower dimensional tori in planetary systems
    37 schema:pagination 397-424
    38 schema:productId N39b81870379349d9bc7bd87e230ecef0
    39 N490768de85e641dabf633bf28c0b9d87
    40 Na37c319cb22b4b9e8e5ab1b0100f10ba
    41 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035910283
    42 https://doi.org/10.1007/s10569-014-9562-7
    43 schema:sdDatePublished 2019-04-10T19:57
    44 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    45 schema:sdPublisher N4000c675461349e485f92a172a168b35
    46 schema:url http://link.springer.com/10.1007%2Fs10569-014-9562-7
    47 sgo:license sg:explorer/license/
    48 sgo:sdDataset articles
    49 rdf:type schema:ScholarlyArticle
    50 N12b4993ff3c842bfa99cfdb0c29c09dc schema:issueNumber 3-4
    51 rdf:type schema:PublicationIssue
    52 N39b81870379349d9bc7bd87e230ecef0 schema:name doi
    53 schema:value 10.1007/s10569-014-9562-7
    54 rdf:type schema:PropertyValue
    55 N3f5740bb22d7457c8ac17c44b1c1ef75 rdf:first sg:person.07637253565.17
    56 rdf:rest Nac3efb890339482191408271de290f2d
    57 N4000c675461349e485f92a172a168b35 schema:name Springer Nature - SN SciGraph project
    58 rdf:type schema:Organization
    59 N490768de85e641dabf633bf28c0b9d87 schema:name readcube_id
    60 schema:value ab10a9972e863fb11ea2987328c8472548a9c0b026192058bbdbf2f0f7c3a125
    61 rdf:type schema:PropertyValue
    62 N8ccbf169f20941e1bbcfe3bb41beadad rdf:first sg:person.010532704656.30
    63 rdf:rest N3f5740bb22d7457c8ac17c44b1c1ef75
    64 Na37c319cb22b4b9e8e5ab1b0100f10ba schema:name dimensions_id
    65 schema:value pub.1035910283
    66 rdf:type schema:PropertyValue
    67 Nac3efb890339482191408271de290f2d rdf:first sg:person.012027575165.98
    68 rdf:rest rdf:nil
    69 Ne264c7038cc04f1d84f57921f48d7add schema:volumeNumber 119
    70 rdf:type schema:PublicationVolume
    71 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    72 schema:name Mathematical Sciences
    73 rdf:type schema:DefinedTerm
    74 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    75 schema:name Pure Mathematics
    76 rdf:type schema:DefinedTerm
    77 sg:journal.1136436 schema:issn 0008-8714
    78 0923-2958
    79 schema:name Celestial Mechanics and Dynamical Astronomy
    80 rdf:type schema:Periodical
    81 sg:person.010532704656.30 schema:affiliation https://www.grid.ac/institutes/grid.4708.b
    82 schema:familyName Giorgilli
    83 schema:givenName Antonio
    84 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010532704656.30
    85 rdf:type schema:Person
    86 sg:person.012027575165.98 schema:affiliation https://www.grid.ac/institutes/grid.6520.1
    87 schema:familyName Sansottera
    88 schema:givenName Marco
    89 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012027575165.98
    90 rdf:type schema:Person
    91 sg:person.07637253565.17 schema:affiliation https://www.grid.ac/institutes/grid.6530.0
    92 schema:familyName Locatelli
    93 schema:givenName Ugo
    94 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07637253565.17
    95 rdf:type schema:Person
    96 sg:pub.10.1007/978-94-011-4673-9_8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025219621
    97 https://doi.org/10.1007/978-94-011-4673-9_8
    98 rdf:type schema:CreativeWork
    99 sg:pub.10.1007/bf01221590 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013571657
    100 https://doi.org/10.1007/bf01221590
    101 rdf:type schema:CreativeWork
    102 sg:pub.10.1007/bf01227790 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001288867
    103 https://doi.org/10.1007/bf01227790
    104 rdf:type schema:CreativeWork
    105 sg:pub.10.1007/bf02108809 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046115209
    106 https://doi.org/10.1007/bf02108809
    107 rdf:type schema:CreativeWork
    108 sg:pub.10.1007/bf02180145 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004400049
    109 https://doi.org/10.1007/bf02180145
    110 rdf:type schema:CreativeWork
    111 sg:pub.10.1007/pl00001462 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021394303
    112 https://doi.org/10.1007/pl00001462
    113 rdf:type schema:CreativeWork
    114 sg:pub.10.1007/pl00001475 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042122109
    115 https://doi.org/10.1007/pl00001475
    116 rdf:type schema:CreativeWork
    117 sg:pub.10.1007/s00205-003-0269-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008228544
    118 https://doi.org/10.1007/s00205-003-0269-2
    119 rdf:type schema:CreativeWork
    120 sg:pub.10.1007/s00220-011-1264-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009792688
    121 https://doi.org/10.1007/s00220-011-1264-3
    122 rdf:type schema:CreativeWork
    123 sg:pub.10.1007/s10231-014-0408-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011031562
    124 https://doi.org/10.1007/s10231-014-0408-4
    125 rdf:type schema:CreativeWork
    126 sg:pub.10.1007/s10569-009-9192-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021916524
    127 https://doi.org/10.1007/s10569-009-9192-7
    128 rdf:type schema:CreativeWork
    129 sg:pub.10.1007/s10569-011-9375-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1024463109
    130 https://doi.org/10.1007/s10569-011-9375-x
    131 rdf:type schema:CreativeWork
    132 sg:pub.10.1007/s10569-013-9501-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1017966435
    133 https://doi.org/10.1007/s10569-013-9501-z
    134 rdf:type schema:CreativeWork
    135 sg:pub.10.1023/a:1011139523256 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009130340
    136 https://doi.org/10.1023/a:1011139523256
    137 rdf:type schema:CreativeWork
    138 https://doi.org/10.1016/j.matcom.2010.11.018 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039296165
    139 rdf:type schema:CreativeWork
    140 https://doi.org/10.1070/rm1963v018n06abeh001143 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058193727
    141 rdf:type schema:CreativeWork
    142 https://doi.org/10.1070/rm1977v032n06abeh003859 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058194264
    143 rdf:type schema:CreativeWork
    144 https://doi.org/10.1070/sm1989v064n02abeh003316 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058200759
    145 rdf:type schema:CreativeWork
    146 https://doi.org/10.1086/109964 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058448574
    147 rdf:type schema:CreativeWork
    148 https://doi.org/10.1137/s0036141004443646 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062876034
    149 rdf:type schema:CreativeWork
    150 https://doi.org/10.1142/s0129055x96000135 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062898633
    151 rdf:type schema:CreativeWork
    152 https://doi.org/10.3934/dcdsb.2007.7.377 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071736148
    153 rdf:type schema:CreativeWork
    154 https://doi.org/10.3934/dcdss.2010.3.601 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071737698
    155 rdf:type schema:CreativeWork
    156 https://www.grid.ac/institutes/grid.4708.b schema:alternateName University of Milan
    157 schema:name Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, 20133, Milano, Italy
    158 rdf:type schema:Organization
    159 https://www.grid.ac/institutes/grid.6520.1 schema:alternateName University of Namur
    160 schema:name Département de Mathématique and NAXYS, Université de Namur, Rempart de la Vierge 8, 5000, Namur, Belgium
    161 rdf:type schema:Organization
    162 https://www.grid.ac/institutes/grid.6530.0 schema:alternateName University of Rome Tor Vergata
    163 schema:name Dipartimento di Matematica, Università degli Studi di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Roma, Italy
    164 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...