Estimates for normal forms of differential equations near an equilibrium point View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1988-09

AUTHORS

Antonio Giorgilli, Andrea Posilicano

ABSTRACT

We consider the problem of finding a normal form for differential equations in the neighbourhood of an equilibrium point, and produce general explicit estimates for both the normal form at a finite order and the remainder, using the method of Lie transforms. With such technique, the classical Poincaré-Dulac theorems are recovered, and the problem of the stability of a reversible system of coupled harmonic oscillators up to exponentially large times is discussed. More... »

PAGES

713-732

References to SciGraph publications

  • 1986. Lie series, Lie transformations, and their applications in LIE METHODS IN OPTICS
  • 1985-10. Rigorous estimates for the series expansions of Hamiltonian perturbation theory in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1973. The Algorithm of the Inverse for Lie Transform in RECENT ADVANCES IN DYNAMICAL ASTRONOMY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf00948732

    DOI

    http://dx.doi.org/10.1007/bf00948732

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1026706993


    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": {
              "name": [
                "Dipartimento di Fisica dell'Universit\u00e0, Via Celoria 16, 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": {
              "name": [
                "Dipartimento di Fisica dell'Universit\u00e0, Via Celoria 16, 20133, Milano, Italy"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Posilicano", 
            "givenName": "Andrea", 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/3-540-16471-5_3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003511755", 
              "https://doi.org/10.1007/3-540-16471-5_3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01230921", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020743826", 
              "https://doi.org/10.1007/bf01230921"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01230921", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020743826", 
              "https://doi.org/10.1007/bf01230921"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-94-010-2611-6_26", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040699962", 
              "https://doi.org/10.1007/978-94-010-2611-6_26"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1070/rm1977v032n06abeh003859", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058194264"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.24033/bsmf.910", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1083662516"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1988-09", 
        "datePublishedReg": "1988-09-01", 
        "description": "We consider the problem of finding a normal form for differential equations in the neighbourhood of an equilibrium point, and produce general explicit estimates for both the normal form at a finite order and the remainder, using the method of Lie transforms. With such technique, the classical Poincar\u00e9-Dulac theorems are recovered, and the problem of the stability of a reversible system of coupled harmonic oscillators up to exponentially large times is discussed.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/bf00948732", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1053636", 
            "issn": [
              "0044-2275", 
              "1420-9039"
            ], 
            "name": "Zeitschrift f\u00fcr angewandte Mathematik und Physik", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "5", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "39"
          }
        ], 
        "name": "Estimates for normal forms of differential equations near an equilibrium point", 
        "pagination": "713-732", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "7f3afd28271d89155265356059daf3b0502fde3d6785ac66ff8a7d59855c337e"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/bf00948732"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1026706993"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/bf00948732", 
          "https://app.dimensions.ai/details/publication/pub.1026706993"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T13:27", 
        "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/v90/0000000370_0000000370/records_46738_00000001.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007%2FBF00948732"
      }
    ]
     

    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/bf00948732'

    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/bf00948732'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf00948732'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf00948732'


     

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

    86 TRIPLES      21 PREDICATES      32 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf00948732 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author Nb7720799848e4b1d955dcb3bf14ad6d8
    4 schema:citation sg:pub.10.1007/3-540-16471-5_3
    5 sg:pub.10.1007/978-94-010-2611-6_26
    6 sg:pub.10.1007/bf01230921
    7 https://doi.org/10.1070/rm1977v032n06abeh003859
    8 https://doi.org/10.24033/bsmf.910
    9 schema:datePublished 1988-09
    10 schema:datePublishedReg 1988-09-01
    11 schema:description We consider the problem of finding a normal form for differential equations in the neighbourhood of an equilibrium point, and produce general explicit estimates for both the normal form at a finite order and the remainder, using the method of Lie transforms. With such technique, the classical Poincaré-Dulac theorems are recovered, and the problem of the stability of a reversible system of coupled harmonic oscillators up to exponentially large times is discussed.
    12 schema:genre research_article
    13 schema:inLanguage en
    14 schema:isAccessibleForFree false
    15 schema:isPartOf N404502082dd64820bb3796720fe778b6
    16 Nac775d50171e4d2bacee83c7f96e5c85
    17 sg:journal.1053636
    18 schema:name Estimates for normal forms of differential equations near an equilibrium point
    19 schema:pagination 713-732
    20 schema:productId N39155c0b962d4b73959e366a4fe9a65a
    21 N61e541cfce074d6b9f9379936a85600e
    22 Ne87b9c63f51f4e3985a2ed0c4eb0f169
    23 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026706993
    24 https://doi.org/10.1007/bf00948732
    25 schema:sdDatePublished 2019-04-11T13:27
    26 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    27 schema:sdPublisher N1672cb4724e44aeba8cae8318dcc3bdd
    28 schema:url http://link.springer.com/10.1007%2FBF00948732
    29 sgo:license sg:explorer/license/
    30 sgo:sdDataset articles
    31 rdf:type schema:ScholarlyArticle
    32 N1672cb4724e44aeba8cae8318dcc3bdd schema:name Springer Nature - SN SciGraph project
    33 rdf:type schema:Organization
    34 N39155c0b962d4b73959e366a4fe9a65a schema:name dimensions_id
    35 schema:value pub.1026706993
    36 rdf:type schema:PropertyValue
    37 N404502082dd64820bb3796720fe778b6 schema:volumeNumber 39
    38 rdf:type schema:PublicationVolume
    39 N40a2adedcaad4a1d87e0188271137ef3 schema:affiliation Nca98dc8b5fe347e099af43ce6816a7d5
    40 schema:familyName Posilicano
    41 schema:givenName Andrea
    42 rdf:type schema:Person
    43 N5576a0ef86634279a09319961bc079a0 rdf:first N40a2adedcaad4a1d87e0188271137ef3
    44 rdf:rest rdf:nil
    45 N61e541cfce074d6b9f9379936a85600e schema:name readcube_id
    46 schema:value 7f3afd28271d89155265356059daf3b0502fde3d6785ac66ff8a7d59855c337e
    47 rdf:type schema:PropertyValue
    48 N70af64ef513f492695af86af60ab5e59 schema:name Dipartimento di Fisica dell'Università, Via Celoria 16, 20133, Milano, Italy
    49 rdf:type schema:Organization
    50 Nac775d50171e4d2bacee83c7f96e5c85 schema:issueNumber 5
    51 rdf:type schema:PublicationIssue
    52 Nb7720799848e4b1d955dcb3bf14ad6d8 rdf:first sg:person.010532704656.30
    53 rdf:rest N5576a0ef86634279a09319961bc079a0
    54 Nca98dc8b5fe347e099af43ce6816a7d5 schema:name Dipartimento di Fisica dell'Università, Via Celoria 16, 20133, Milano, Italy
    55 rdf:type schema:Organization
    56 Ne87b9c63f51f4e3985a2ed0c4eb0f169 schema:name doi
    57 schema:value 10.1007/bf00948732
    58 rdf:type schema:PropertyValue
    59 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    60 schema:name Mathematical Sciences
    61 rdf:type schema:DefinedTerm
    62 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    63 schema:name Pure Mathematics
    64 rdf:type schema:DefinedTerm
    65 sg:journal.1053636 schema:issn 0044-2275
    66 1420-9039
    67 schema:name Zeitschrift für angewandte Mathematik und Physik
    68 rdf:type schema:Periodical
    69 sg:person.010532704656.30 schema:affiliation N70af64ef513f492695af86af60ab5e59
    70 schema:familyName Giorgilli
    71 schema:givenName Antonio
    72 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010532704656.30
    73 rdf:type schema:Person
    74 sg:pub.10.1007/3-540-16471-5_3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003511755
    75 https://doi.org/10.1007/3-540-16471-5_3
    76 rdf:type schema:CreativeWork
    77 sg:pub.10.1007/978-94-010-2611-6_26 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040699962
    78 https://doi.org/10.1007/978-94-010-2611-6_26
    79 rdf:type schema:CreativeWork
    80 sg:pub.10.1007/bf01230921 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020743826
    81 https://doi.org/10.1007/bf01230921
    82 rdf:type schema:CreativeWork
    83 https://doi.org/10.1070/rm1977v032n06abeh003859 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058194264
    84 rdf:type schema:CreativeWork
    85 https://doi.org/10.24033/bsmf.910 schema:sameAs https://app.dimensions.ai/details/publication/pub.1083662516
    86 rdf:type schema:CreativeWork
     




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


    ...