Measures of maximal entropy for surface diffeomorphisms

Measures of maximal entropy for surface diffeomorphisms

We show that $C^\infty$ surface diffeomorphisms with positive topological entropy have at most finitely many ergodic measures of maximal entropy in general, and at most one in the topologically transitive case. This answers a question of Newhouse, who proved that such measures always exist. To do th...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Annals of mathematics 2022-03, Vol.195 (2), p.421-508
Hauptverfasser: Buzzi, Jérôme, Crovisier, Sylvain, Sarig, Omri
Format: Artikel
Sprache:eng
Schlagworte:
Dynamical Systems
Mathematics
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 508
container_issue 2
container_start_page 421
container_title Annals of mathematics
container_volume 195
creator Buzzi, Jérôme
Crovisier, Sylvain
Sarig, Omri
description We show that $C^\infty$ surface diffeomorphisms with positive topological entropy have at most finitely many ergodic measures of maximal entropy in general, and at most one in the topologically transitive case. This answers a question of Newhouse, who proved that such measures always exist. To do this we generalize Smale's spectral decomposition theorem to non-uniformly hyperbolic surface diffeomorphisms, we introduce homoclinic classes of measures, and we study their properties using codings by irreducible countable state Markov shifts.
doi_str_mv 10.4007/annals.2022.195.2.2
format Article
fullrecord <record><control><sourceid>hal_cross</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_02367519v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>oai_HAL_hal_02367519v1</sourcerecordid><originalsourceid>FETCH-LOGICAL-c283t-b8514d73677473c15748df542b7776ffa470c2c6f95ba3b50c348e20fa77d6943</originalsourceid><addsrcrecordid>eNo9kE9PwzAMxXMAiTH4BFx65dCSv3V7nCZgk4q4gMQtStNYK2qbKhmIfXsyFXGybD-_Z_0IuWO0kJTCg5kmM8SCU84LVquCF_yCrCilIpdV-XFFrmP8TC1ACSsCL87Er-Bi5jEbzU8_miFz0zH4-ZShD1laorEu63pE50cf5kMfx3hDLjHFuNu_uibvT49v213evD7vt5smt7wSx7ytFJMdiBJAgrBMgaw6VJK3kPIRjQRquS2xVq0RraJWyMpxigagK2sp1uR-8T2YQc8hvRdO2pte7zaNPs8oT-aK1d8sacWitcHHGBz-HzCqz2z0wkaf2ejERnPNxS_mSlp-</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Measures of maximal entropy for surface diffeomorphisms</title><source>Alma/SFX Local Collection</source><creator>Buzzi, Jérôme ; Crovisier, Sylvain ; Sarig, Omri</creator><creatorcontrib>Buzzi, Jérôme ; Crovisier, Sylvain ; Sarig, Omri</creatorcontrib><description>We show that $C^\infty$ surface diffeomorphisms with positive topological entropy have at most finitely many ergodic measures of maximal entropy in general, and at most one in the topologically transitive case. This answers a question of Newhouse, who proved that such measures always exist. To do this we generalize Smale's spectral decomposition theorem to non-uniformly hyperbolic surface diffeomorphisms, we introduce homoclinic classes of measures, and we study their properties using codings by irreducible countable state Markov shifts.</description><identifier>ISSN: 0003-486X</identifier><identifier>DOI: 10.4007/annals.2022.195.2.2</identifier><language>eng</language><publisher>Princeton University, Department of Mathematics</publisher><subject>Dynamical Systems ; Mathematics</subject><ispartof>Annals of mathematics, 2022-03, Vol.195 (2), p.421-508</ispartof><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c283t-b8514d73677473c15748df542b7776ffa470c2c6f95ba3b50c348e20fa77d6943</citedby><orcidid>0000-0002-8559-4359</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,776,780,881,27903,27904</link.rule.ids><backlink>$$Uhttps://hal.science/hal-02367519$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Buzzi, Jérôme</creatorcontrib><creatorcontrib>Crovisier, Sylvain</creatorcontrib><creatorcontrib>Sarig, Omri</creatorcontrib><title>Measures of maximal entropy for surface diffeomorphisms</title><title>Annals of mathematics</title><description>We show that $C^\infty$ surface diffeomorphisms with positive topological entropy have at most finitely many ergodic measures of maximal entropy in general, and at most one in the topologically transitive case. This answers a question of Newhouse, who proved that such measures always exist. To do this we generalize Smale's spectral decomposition theorem to non-uniformly hyperbolic surface diffeomorphisms, we introduce homoclinic classes of measures, and we study their properties using codings by irreducible countable state Markov shifts.</description><subject>Dynamical Systems</subject><subject>Mathematics</subject><issn>0003-486X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNo9kE9PwzAMxXMAiTH4BFx65dCSv3V7nCZgk4q4gMQtStNYK2qbKhmIfXsyFXGybD-_Z_0IuWO0kJTCg5kmM8SCU84LVquCF_yCrCilIpdV-XFFrmP8TC1ACSsCL87Er-Bi5jEbzU8_miFz0zH4-ZShD1laorEu63pE50cf5kMfx3hDLjHFuNu_uibvT49v213evD7vt5smt7wSx7ytFJMdiBJAgrBMgaw6VJK3kPIRjQRquS2xVq0RraJWyMpxigagK2sp1uR-8T2YQc8hvRdO2pte7zaNPs8oT-aK1d8sacWitcHHGBz-HzCqz2z0wkaf2ejERnPNxS_mSlp-</recordid><startdate>20220301</startdate><enddate>20220301</enddate><creator>Buzzi, Jérôme</creator><creator>Crovisier, Sylvain</creator><creator>Sarig, Omri</creator><general>Princeton University, Department of Mathematics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-8559-4359</orcidid></search><sort><creationdate>20220301</creationdate><title>Measures of maximal entropy for surface diffeomorphisms</title><author>Buzzi, Jérôme ; Crovisier, Sylvain ; Sarig, Omri</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c283t-b8514d73677473c15748df542b7776ffa470c2c6f95ba3b50c348e20fa77d6943</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Dynamical Systems</topic><topic>Mathematics</topic><toplevel>online_resources</toplevel><creatorcontrib>Buzzi, Jérôme</creatorcontrib><creatorcontrib>Crovisier, Sylvain</creatorcontrib><creatorcontrib>Sarig, Omri</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Annals of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Buzzi, Jérôme</au><au>Crovisier, Sylvain</au><au>Sarig, Omri</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Measures of maximal entropy for surface diffeomorphisms</atitle><jtitle>Annals of mathematics</jtitle><date>2022-03-01</date><risdate>2022</risdate><volume>195</volume><issue>2</issue><spage>421</spage><epage>508</epage><pages>421-508</pages><issn>0003-486X</issn><abstract>We show that $C^\infty$ surface diffeomorphisms with positive topological entropy have at most finitely many ergodic measures of maximal entropy in general, and at most one in the topologically transitive case. This answers a question of Newhouse, who proved that such measures always exist. To do this we generalize Smale's spectral decomposition theorem to non-uniformly hyperbolic surface diffeomorphisms, we introduce homoclinic classes of measures, and we study their properties using codings by irreducible countable state Markov shifts.</abstract><pub>Princeton University, Department of Mathematics</pub><doi>10.4007/annals.2022.195.2.2</doi><tpages>88</tpages><orcidid>https://orcid.org/0000-0002-8559-4359</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 0003-486X
ispartof Annals of mathematics, 2022-03, Vol.195 (2), p.421-508
issn 0003-486X
language eng
recordid cdi_hal_primary_oai_HAL_hal_02367519v1
source Alma/SFX Local Collection
subjects Dynamical Systems
Mathematics
title Measures of maximal entropy for surface diffeomorphisms
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-21T17%3A27%3A55IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-hal_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Measures%20of%20maximal%20entropy%20for%20surface%20diffeomorphisms&rft.jtitle=Annals%20of%20mathematics&rft.au=Buzzi,%20J%C3%A9r%C3%B4me&rft.date=2022-03-01&rft.volume=195&rft.issue=2&rft.spage=421&rft.epage=508&rft.pages=421-508&rft.issn=0003-486X&rft_id=info:doi/10.4007/annals.2022.195.2.2&rft_dat=%3Chal_cross%3Eoai_HAL_hal_02367519v1%3C/hal_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true