Thouvenot’s Isomorphism Problem for Tensor Powers of Ergodic Flows View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2018-11

AUTHORS

V. V. Ryzhikov

ABSTRACT

Let S and T be automorphisms of a probability space whose powers S ⊗ S and T ⊗ T isomorphic. Are the automorphisms S and T isomorphičThis question of Thouvenot is well known in ergodic theory. We answer this question and generalize a result of Kulaga concerning isomorphism in the case of flows. We show that if weakly mixing flows St ⊗ St and Tt ⊗ Tt are isomorphic, then so are the flows St and Tt, provided that one of them has a weak integral limit. More... »

PAGES

900-904

References to SciGraph publications

  • 2012-04. A note on the isomorphism of Cartesian products of ergodic flows in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • Journal

    TITLE

    Mathematical Notes

    ISSUE

    5-6

    VOLUME

    104

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1134/s0001434618110330

    DOI

    http://dx.doi.org/10.1134/s0001434618110330

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1110980192


    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/2008/0915", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Interdisciplinary Engineering", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/09", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Engineering", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "name": [
                "LomonosovMoscow State University, 119991, Moscow, Russia"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Ryzhikov", 
            "givenName": "V. V.", 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/s10883-012-9142-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046682345", 
              "https://doi.org/10.1007/s10883-012-9142-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/proc/12906", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059345239"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4213/faa3207", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072363781"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4213/mzm10157", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072365241"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4213/mzm10517", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072365534"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4213/mzm10965", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072365795"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4213/mzm1757", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072366646"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4213/mzm3527", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072367421"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4213/sm1497", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072371558"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4213/mzm11768", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1093147856"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4213/sm8932", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1103652951"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2018-11", 
        "datePublishedReg": "2018-11-01", 
        "description": "Let S and T be automorphisms of a probability space whose powers S \u2297 S and T \u2297 T isomorphic. Are the automorphisms S and T isomorphi\u010dThis question of Thouvenot is well known in ergodic theory. We answer this question and generalize a result of Kulaga concerning isomorphism in the case of flows. We show that if weakly mixing flows St \u2297 St and Tt \u2297 Tt are isomorphic, then so are the flows St and Tt, provided that one of them has a weak integral limit.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1134/s0001434618110330", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136530", 
            "issn": [
              "1757-7489", 
              "1573-8876"
            ], 
            "name": "Mathematical Notes", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "5-6", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "104"
          }
        ], 
        "name": "Thouvenot\u2019s Isomorphism Problem for Tensor Powers of Ergodic Flows", 
        "pagination": "900-904", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "7b5a9104755ca418378052643a66dd8c2a196613a82c0585047e5d8bd39606da"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1134/s0001434618110330"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1110980192"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1134/s0001434618110330", 
          "https://app.dimensions.ai/details/publication/pub.1110980192"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T08:29", 
        "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/v90/0000000307_0000000307/records_42532_00000000.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1134%2FS0001434618110330"
      }
    ]
     

    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.10.1134/s0001434618110330'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1134/s0001434618110330'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1134/s0001434618110330'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1134/s0001434618110330'


     

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

    93 TRIPLES      21 PREDICATES      38 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1134/s0001434618110330 schema:about anzsrc-for:09
    2 anzsrc-for:0915
    3 schema:author N62b9cc69d9634ccfa07c89a9b97314d6
    4 schema:citation sg:pub.10.1007/s10883-012-9142-7
    5 https://doi.org/10.1090/proc/12906
    6 https://doi.org/10.4213/faa3207
    7 https://doi.org/10.4213/mzm10157
    8 https://doi.org/10.4213/mzm10517
    9 https://doi.org/10.4213/mzm10965
    10 https://doi.org/10.4213/mzm11768
    11 https://doi.org/10.4213/mzm1757
    12 https://doi.org/10.4213/mzm3527
    13 https://doi.org/10.4213/sm1497
    14 https://doi.org/10.4213/sm8932
    15 schema:datePublished 2018-11
    16 schema:datePublishedReg 2018-11-01
    17 schema:description Let S and T be automorphisms of a probability space whose powers S ⊗ S and T ⊗ T isomorphic. Are the automorphisms S and T isomorphičThis question of Thouvenot is well known in ergodic theory. We answer this question and generalize a result of Kulaga concerning isomorphism in the case of flows. We show that if weakly mixing flows St ⊗ St and Tt ⊗ Tt are isomorphic, then so are the flows St and Tt, provided that one of them has a weak integral limit.
    18 schema:genre research_article
    19 schema:inLanguage en
    20 schema:isAccessibleForFree false
    21 schema:isPartOf N26c67ed1ef0f48d2b6c3d057432008fa
    22 Nae7fcb6202bb49c5ad94bfadee5d48de
    23 sg:journal.1136530
    24 schema:name Thouvenot’s Isomorphism Problem for Tensor Powers of Ergodic Flows
    25 schema:pagination 900-904
    26 schema:productId N81ae97f586de4cb7a8f5b6c658c0c7cc
    27 Ncf82098a964c4eb3b6f0e800411933e8
    28 Nfa767e97273044ca8d49f226269d6ee5
    29 schema:sameAs https://app.dimensions.ai/details/publication/pub.1110980192
    30 https://doi.org/10.1134/s0001434618110330
    31 schema:sdDatePublished 2019-04-11T08:29
    32 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    33 schema:sdPublisher Ndf942ba1501e46648bc6126afbf4f98c
    34 schema:url https://link.springer.com/10.1134%2FS0001434618110330
    35 sgo:license sg:explorer/license/
    36 sgo:sdDataset articles
    37 rdf:type schema:ScholarlyArticle
    38 N26c67ed1ef0f48d2b6c3d057432008fa schema:volumeNumber 104
    39 rdf:type schema:PublicationVolume
    40 N36188299f4874d83999efcc620352e04 schema:affiliation Na48f6ea723a54b90b036b4b8a7d98e92
    41 schema:familyName Ryzhikov
    42 schema:givenName V. V.
    43 rdf:type schema:Person
    44 N62b9cc69d9634ccfa07c89a9b97314d6 rdf:first N36188299f4874d83999efcc620352e04
    45 rdf:rest rdf:nil
    46 N81ae97f586de4cb7a8f5b6c658c0c7cc schema:name dimensions_id
    47 schema:value pub.1110980192
    48 rdf:type schema:PropertyValue
    49 Na48f6ea723a54b90b036b4b8a7d98e92 schema:name LomonosovMoscow State University, 119991, Moscow, Russia
    50 rdf:type schema:Organization
    51 Nae7fcb6202bb49c5ad94bfadee5d48de schema:issueNumber 5-6
    52 rdf:type schema:PublicationIssue
    53 Ncf82098a964c4eb3b6f0e800411933e8 schema:name readcube_id
    54 schema:value 7b5a9104755ca418378052643a66dd8c2a196613a82c0585047e5d8bd39606da
    55 rdf:type schema:PropertyValue
    56 Ndf942ba1501e46648bc6126afbf4f98c schema:name Springer Nature - SN SciGraph project
    57 rdf:type schema:Organization
    58 Nfa767e97273044ca8d49f226269d6ee5 schema:name doi
    59 schema:value 10.1134/s0001434618110330
    60 rdf:type schema:PropertyValue
    61 anzsrc-for:09 schema:inDefinedTermSet anzsrc-for:
    62 schema:name Engineering
    63 rdf:type schema:DefinedTerm
    64 anzsrc-for:0915 schema:inDefinedTermSet anzsrc-for:
    65 schema:name Interdisciplinary Engineering
    66 rdf:type schema:DefinedTerm
    67 sg:journal.1136530 schema:issn 1573-8876
    68 1757-7489
    69 schema:name Mathematical Notes
    70 rdf:type schema:Periodical
    71 sg:pub.10.1007/s10883-012-9142-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046682345
    72 https://doi.org/10.1007/s10883-012-9142-7
    73 rdf:type schema:CreativeWork
    74 https://doi.org/10.1090/proc/12906 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059345239
    75 rdf:type schema:CreativeWork
    76 https://doi.org/10.4213/faa3207 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072363781
    77 rdf:type schema:CreativeWork
    78 https://doi.org/10.4213/mzm10157 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072365241
    79 rdf:type schema:CreativeWork
    80 https://doi.org/10.4213/mzm10517 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072365534
    81 rdf:type schema:CreativeWork
    82 https://doi.org/10.4213/mzm10965 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072365795
    83 rdf:type schema:CreativeWork
    84 https://doi.org/10.4213/mzm11768 schema:sameAs https://app.dimensions.ai/details/publication/pub.1093147856
    85 rdf:type schema:CreativeWork
    86 https://doi.org/10.4213/mzm1757 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072366646
    87 rdf:type schema:CreativeWork
    88 https://doi.org/10.4213/mzm3527 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072367421
    89 rdf:type schema:CreativeWork
    90 https://doi.org/10.4213/sm1497 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072371558
    91 rdf:type schema:CreativeWork
    92 https://doi.org/10.4213/sm8932 schema:sameAs https://app.dimensions.ai/details/publication/pub.1103652951
    93 rdf:type schema:CreativeWork
     




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


    ...