Geodesic tracking and the shape of ergodic rotation sets

García-Sassi, Alejo - Guihéneuf, Pierre-Antoine - Lessa Echeverriarza, Pablo

Resumen:

We prove a structure theorem for ergodic homological rotation sets of homeomorphisms isotopic to the identity on a closed orientable hyperbolic surface: this set is made of a finite number of pieces that are either one-dimensional or almost convex. The latter ones give birth to horseshoes; in the case of a zero-entropy homeomorphism we show that there exists a geodesic lamination containing the directions in which generic orbits with respect to ergodic invariant probabilities turn around the surface under iterations of the homeomorphism. The proof is based on the idea of geodesic tracking of orbits that are typical for some invariant measure by geodesics on the surface, that allows to get links between the dynamics of such points and the one of the geodesic flow on some invariant subset of the unit tangent bundle of the surface.


Detalles Bibliográficos
2024
MATHEMATICS - DYNAMICAL SYSTEMS
Inglés
Universidad de la República
COLIBRI
https://hdl.handle.net/20.500.12008/44753
Acceso abierto
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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author García-Sassi, Alejo
author2 Guihéneuf, Pierre-Antoine
Lessa Echeverriarza, Pablo
author2_role author
author
author_facet García-Sassi, Alejo
Guihéneuf, Pierre-Antoine
Lessa Echeverriarza, Pablo
author_role author
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collection COLIBRI
dc.contributor.filiacion.none.fl_str_mv García-Sassi Alejo, Universidad de la República. Facultad de Ciencias. Centro de Matemática
Guihéneuf Pierre-Antoine
Lessa Echeverriarza Pablo, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.
dc.creator.none.fl_str_mv García-Sassi, Alejo
Guihéneuf, Pierre-Antoine
Lessa Echeverriarza, Pablo
dc.date.accessioned.none.fl_str_mv 2024-07-15T12:18:03Z
dc.date.available.none.fl_str_mv 2024-07-15T12:18:03Z
dc.date.issued.none.fl_str_mv 2024
dc.description.abstract.none.fl_txt_mv We prove a structure theorem for ergodic homological rotation sets of homeomorphisms isotopic to the identity on a closed orientable hyperbolic surface: this set is made of a finite number of pieces that are either one-dimensional or almost convex. The latter ones give birth to horseshoes; in the case of a zero-entropy homeomorphism we show that there exists a geodesic lamination containing the directions in which generic orbits with respect to ergodic invariant probabilities turn around the surface under iterations of the homeomorphism. The proof is based on the idea of geodesic tracking of orbits that are typical for some invariant measure by geodesics on the surface, that allows to get links between the dynamics of such points and the one of the geodesic flow on some invariant subset of the unit tangent bundle of the surface.
dc.description.es.fl_txt_mv Disponible también en: HAL science ouverte, 2024. hal-04491543
dc.format.extent.es.fl_str_mv 84 p.
dc.format.mimetype.es.fl_str_mv application/pdf
dc.identifier.citation.es.fl_str_mv García-Sassi, A, Guihéneuf, P y Lessa Echeverriarza, P. "Geodesic tracking and the shape of ergodic rotation sets" [Preprint]. Publicado en: Mathematics (Dynamical Systems). 2024 arXiv:2312.06249v2, mar. 2024, pp. 1-84.
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12008/44753
dc.language.iso.none.fl_str_mv en
eng
dc.publisher.es.fl_str_mv arXiv
dc.relation.ispartof.es.fl_str_mv Mathematics (Dynamical Systems), arXiv:2312.06249v2, mar. 2024, pp. 1-84
dc.rights.license.none.fl_str_mv Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
dc.source.none.fl_str_mv reponame:COLIBRI
instname:Universidad de la República
instacron:Universidad de la República
dc.subject.other.es.fl_str_mv MATHEMATICS - DYNAMICAL SYSTEMS
dc.title.none.fl_str_mv Geodesic tracking and the shape of ergodic rotation sets
dc.type.es.fl_str_mv Preprint
dc.type.none.fl_str_mv info:eu-repo/semantics/preprint
dc.type.version.none.fl_str_mv info:eu-repo/semantics/submittedVersion
description Disponible también en: HAL science ouverte, 2024. hal-04491543
eu_rights_str_mv openAccess
format preprint
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identifier_str_mv García-Sassi, A, Guihéneuf, P y Lessa Echeverriarza, P. "Geodesic tracking and the shape of ergodic rotation sets" [Preprint]. Publicado en: Mathematics (Dynamical Systems). 2024 arXiv:2312.06249v2, mar. 2024, pp. 1-84.
instacron_str Universidad de la República
institution Universidad de la República
instname_str Universidad de la República
language eng
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publishDate 2024
reponame_str COLIBRI
repository.mail.fl_str_mv mabel.seroubian@seciu.edu.uy
repository.name.fl_str_mv COLIBRI - Universidad de la República
repository_id_str 4771
rights_invalid_str_mv Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
spelling García-Sassi Alejo, Universidad de la República. Facultad de Ciencias. Centro de MatemáticaGuihéneuf Pierre-AntoineLessa Echeverriarza Pablo, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.2024-07-15T12:18:03Z2024-07-15T12:18:03Z2024García-Sassi, A, Guihéneuf, P y Lessa Echeverriarza, P. "Geodesic tracking and the shape of ergodic rotation sets" [Preprint]. Publicado en: Mathematics (Dynamical Systems). 2024 arXiv:2312.06249v2, mar. 2024, pp. 1-84.https://hdl.handle.net/20.500.12008/44753Disponible también en: HAL science ouverte, 2024. hal-04491543We prove a structure theorem for ergodic homological rotation sets of homeomorphisms isotopic to the identity on a closed orientable hyperbolic surface: this set is made of a finite number of pieces that are either one-dimensional or almost convex. The latter ones give birth to horseshoes; in the case of a zero-entropy homeomorphism we show that there exists a geodesic lamination containing the directions in which generic orbits with respect to ergodic invariant probabilities turn around the surface under iterations of the homeomorphism. The proof is based on the idea of geodesic tracking of orbits that are typical for some invariant measure by geodesics on the surface, that allows to get links between the dynamics of such points and the one of the geodesic flow on some invariant subset of the unit tangent bundle of the surface.Submitted by Egaña Florencia (florega@gmail.com) on 2024-07-11T18:21:15Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 2312.06249v2.pdf: 1014572 bytes, checksum: bd05cce0d2c69d3276189c149db8a3f2 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2024-07-15T11:42:10Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 2312.06249v2.pdf: 1014572 bytes, checksum: bd05cce0d2c69d3276189c149db8a3f2 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2024-07-15T12:18:03Z (GMT). No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 2312.06249v2.pdf: 1014572 bytes, checksum: bd05cce0d2c69d3276189c149db8a3f2 (MD5) Previous issue date: 202484 p.application/pdfenengarXivMathematics (Dynamical Systems), arXiv:2312.06249v2, mar. 2024, pp. 1-84Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)MATHEMATICS - DYNAMICAL SYSTEMSGeodesic tracking and the shape of ergodic rotation setsPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaGarcía-Sassi, AlejoGuihéneuf, Pierre-AntoineLessa Echeverriarza, PabloLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/44753/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/44753/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse
spellingShingle Geodesic tracking and the shape of ergodic rotation sets
García-Sassi, Alejo
MATHEMATICS - DYNAMICAL SYSTEMS
status_str submittedVersion
title Geodesic tracking and the shape of ergodic rotation sets
title_full Geodesic tracking and the shape of ergodic rotation sets
title_fullStr Geodesic tracking and the shape of ergodic rotation sets
title_full_unstemmed Geodesic tracking and the shape of ergodic rotation sets
title_short Geodesic tracking and the shape of ergodic rotation sets
title_sort Geodesic tracking and the shape of ergodic rotation sets
topic MATHEMATICS - DYNAMICAL SYSTEMS
url https://hdl.handle.net/20.500.12008/44753

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