Chaos in Cartan foliations

Chaos in Cartan foliations

Chaotic foliations generalize Devaney’s concept of chaos for dynamical systems. The property of a foliation to be chaotic is transversal, i.e, depends on the structure of the leaf space of the foliation. The transversal structure of a Cartan foliation is modeled on a Cartan manifold. The problem of...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Chaos (Woodbury, N.Y.) N.Y.), 2020-10, Vol.30 (10), p.103116-103116
Hauptverfasser: Bazaikin, Yaroslav V., Galaev, Anton S., Zhukova, Nina I.
Format: Artikel
Sprache:eng
Schlagworte:
Automorphisms
Chaos theory
Manifolds
Subgroups
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 103116
container_issue 10
container_start_page 103116
container_title Chaos (Woodbury, N.Y.)
container_volume 30
creator Bazaikin, Yaroslav V.
Galaev, Anton S.
Zhukova, Nina I.
description Chaotic foliations generalize Devaney’s concept of chaos for dynamical systems. The property of a foliation to be chaotic is transversal, i.e, depends on the structure of the leaf space of the foliation. The transversal structure of a Cartan foliation is modeled on a Cartan manifold. The problem of investigating chaotic Cartan foliations is reduced to the corresponding problem for their holonomy pseudogroups of local automorphisms of transversal Cartan manifolds. For a Cartan foliation of a wide class, this problem is reduced to the corresponding problem for its global holonomy group, which is a countable discrete subgroup of the Lie automorphism group of an associated simply connected Cartan manifold. Several types of Cartan foliations that cannot be chaotic are indicated. Examples of chaotic Cartan foliations are constructed.
doi_str_mv 10.1063/5.0021596
format Article
fullrecord <record><control><sourceid>proquest_scita</sourceid><recordid>TN_cdi_proquest_miscellaneous_2457286021</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2457286021</sourcerecordid><originalsourceid>FETCH-LOGICAL-c360t-f55ee10d02fdbab264d3b5da74241351e266b8c046c249ad5a3a041df39d40483</originalsourceid><addsrcrecordid>eNqd0E1LxDAQBuAgCq6rB6-eCl5U6DqZfDQ9SvELFrzoOaRNil26TU26gv_e1i4IHj3NHB6GeV9CzimsKEh2K1YASEUuD8iCgsrTTCo8nHbBUyoAjslJjBsAoMjEglwU78bHpOmSwoTBdEnt28YMje_iKTmqTRvd2X4uydvD_WvxlK5fHp-Lu3VaMQlDWgvhHAULWNvSlCi5ZaWwJuPIKRPUoZSlqoDLCnlurDDMAKe2ZrnlwBVbkqv5bh_8x87FQW-bWLm2NZ3zu6iRiwyVHGON9PIP3fhd6MbvJoVIlUIY1fWsquBjDK7WfWi2JnxpCnpqSQu9b2m0N7ONVTP85P4f_vThF-p-TPcN_l9x6A</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2452218820</pqid></control><display><type>article</type><title>Chaos in Cartan foliations</title><source>AIP Journals Complete</source><source>Alma/SFX Local Collection</source><creator>Bazaikin, Yaroslav V. ; Galaev, Anton S. ; Zhukova, Nina I.</creator><creatorcontrib>Bazaikin, Yaroslav V. ; Galaev, Anton S. ; Zhukova, Nina I.</creatorcontrib><description>Chaotic foliations generalize Devaney’s concept of chaos for dynamical systems. The property of a foliation to be chaotic is transversal, i.e, depends on the structure of the leaf space of the foliation. The transversal structure of a Cartan foliation is modeled on a Cartan manifold. The problem of investigating chaotic Cartan foliations is reduced to the corresponding problem for their holonomy pseudogroups of local automorphisms of transversal Cartan manifolds. For a Cartan foliation of a wide class, this problem is reduced to the corresponding problem for its global holonomy group, which is a countable discrete subgroup of the Lie automorphism group of an associated simply connected Cartan manifold. Several types of Cartan foliations that cannot be chaotic are indicated. Examples of chaotic Cartan foliations are constructed.</description><identifier>ISSN: 1054-1500</identifier><identifier>EISSN: 1089-7682</identifier><identifier>DOI: 10.1063/5.0021596</identifier><identifier>CODEN: CHAOEH</identifier><language>eng</language><publisher>Melville: American Institute of Physics</publisher><subject>Automorphisms ; Chaos theory ; Manifolds ; Subgroups</subject><ispartof>Chaos (Woodbury, N.Y.), 2020-10, Vol.30 (10), p.103116-103116</ispartof><rights>Author(s)</rights><rights>2020 Author(s). Published under license by AIP Publishing.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c360t-f55ee10d02fdbab264d3b5da74241351e266b8c046c249ad5a3a041df39d40483</citedby><cites>FETCH-LOGICAL-c360t-f55ee10d02fdbab264d3b5da74241351e266b8c046c249ad5a3a041df39d40483</cites><orcidid>0000-0003-3043-4224 ; 0000-0002-4553-559X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,790,4497,27903,27904</link.rule.ids></links><search><creatorcontrib>Bazaikin, Yaroslav V.</creatorcontrib><creatorcontrib>Galaev, Anton S.</creatorcontrib><creatorcontrib>Zhukova, Nina I.</creatorcontrib><title>Chaos in Cartan foliations</title><title>Chaos (Woodbury, N.Y.)</title><description>Chaotic foliations generalize Devaney’s concept of chaos for dynamical systems. The property of a foliation to be chaotic is transversal, i.e, depends on the structure of the leaf space of the foliation. The transversal structure of a Cartan foliation is modeled on a Cartan manifold. The problem of investigating chaotic Cartan foliations is reduced to the corresponding problem for their holonomy pseudogroups of local automorphisms of transversal Cartan manifolds. For a Cartan foliation of a wide class, this problem is reduced to the corresponding problem for its global holonomy group, which is a countable discrete subgroup of the Lie automorphism group of an associated simply connected Cartan manifold. Several types of Cartan foliations that cannot be chaotic are indicated. Examples of chaotic Cartan foliations are constructed.</description><subject>Automorphisms</subject><subject>Chaos theory</subject><subject>Manifolds</subject><subject>Subgroups</subject><issn>1054-1500</issn><issn>1089-7682</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNqd0E1LxDAQBuAgCq6rB6-eCl5U6DqZfDQ9SvELFrzoOaRNil26TU26gv_e1i4IHj3NHB6GeV9CzimsKEh2K1YASEUuD8iCgsrTTCo8nHbBUyoAjslJjBsAoMjEglwU78bHpOmSwoTBdEnt28YMje_iKTmqTRvd2X4uydvD_WvxlK5fHp-Lu3VaMQlDWgvhHAULWNvSlCi5ZaWwJuPIKRPUoZSlqoDLCnlurDDMAKe2ZrnlwBVbkqv5bh_8x87FQW-bWLm2NZ3zu6iRiwyVHGON9PIP3fhd6MbvJoVIlUIY1fWsquBjDK7WfWi2JnxpCnpqSQu9b2m0N7ONVTP85P4f_vThF-p-TPcN_l9x6A</recordid><startdate>202010</startdate><enddate>202010</enddate><creator>Bazaikin, Yaroslav V.</creator><creator>Galaev, Anton S.</creator><creator>Zhukova, Nina I.</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0003-3043-4224</orcidid><orcidid>https://orcid.org/0000-0002-4553-559X</orcidid></search><sort><creationdate>202010</creationdate><title>Chaos in Cartan foliations</title><author>Bazaikin, Yaroslav V. ; Galaev, Anton S. ; Zhukova, Nina I.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c360t-f55ee10d02fdbab264d3b5da74241351e266b8c046c249ad5a3a041df39d40483</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Automorphisms</topic><topic>Chaos theory</topic><topic>Manifolds</topic><topic>Subgroups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bazaikin, Yaroslav V.</creatorcontrib><creatorcontrib>Galaev, Anton S.</creatorcontrib><creatorcontrib>Zhukova, Nina I.</creatorcontrib><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>MEDLINE - Academic</collection><jtitle>Chaos (Woodbury, N.Y.)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bazaikin, Yaroslav V.</au><au>Galaev, Anton S.</au><au>Zhukova, Nina I.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Chaos in Cartan foliations</atitle><jtitle>Chaos (Woodbury, N.Y.)</jtitle><date>2020-10</date><risdate>2020</risdate><volume>30</volume><issue>10</issue><spage>103116</spage><epage>103116</epage><pages>103116-103116</pages><issn>1054-1500</issn><eissn>1089-7682</eissn><coden>CHAOEH</coden><abstract>Chaotic foliations generalize Devaney’s concept of chaos for dynamical systems. The property of a foliation to be chaotic is transversal, i.e, depends on the structure of the leaf space of the foliation. The transversal structure of a Cartan foliation is modeled on a Cartan manifold. The problem of investigating chaotic Cartan foliations is reduced to the corresponding problem for their holonomy pseudogroups of local automorphisms of transversal Cartan manifolds. For a Cartan foliation of a wide class, this problem is reduced to the corresponding problem for its global holonomy group, which is a countable discrete subgroup of the Lie automorphism group of an associated simply connected Cartan manifold. Several types of Cartan foliations that cannot be chaotic are indicated. Examples of chaotic Cartan foliations are constructed.</abstract><cop>Melville</cop><pub>American Institute of Physics</pub><doi>10.1063/5.0021596</doi><tpages>9</tpages><orcidid>https://orcid.org/0000-0003-3043-4224</orcidid><orcidid>https://orcid.org/0000-0002-4553-559X</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 1054-1500
ispartof Chaos (Woodbury, N.Y.), 2020-10, Vol.30 (10), p.103116-103116
issn 1054-1500
1089-7682
language eng
recordid cdi_proquest_miscellaneous_2457286021
source AIP Journals Complete; Alma/SFX Local Collection
subjects Automorphisms
Chaos theory
Manifolds
Subgroups
title Chaos in Cartan foliations
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-21T18%3A49%3A53IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_scita&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Chaos%20in%20Cartan%20foliations&rft.jtitle=Chaos%20(Woodbury,%20N.Y.)&rft.au=Bazaikin,%20Yaroslav%20V.&rft.date=2020-10&rft.volume=30&rft.issue=10&rft.spage=103116&rft.epage=103116&rft.pages=103116-103116&rft.issn=1054-1500&rft.eissn=1089-7682&rft.coden=CHAOEH&rft_id=info:doi/10.1063/5.0021596&rft_dat=%3Cproquest_scita%3E2457286021%3C/proquest_scita%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2452218820&rft_id=info:pmid/&rfr_iscdi=true