Invariant sets for homeomorphisms of hyperbolic 3-manifolds
Resumen:
We prove that under some assumptions on how points escape to infinity in the universal cover, homeomorphisms of hyperbolic 3-manifolds are forced to have several invariant sets (in particular, they cannot be minimal). For this, we use some shadowing techniques which, when the homeomorphism has positive speed with respect to a uniform foliation, allow us to obtain strong consequences on the structure of the invariant sets. We discuss also homological rotation sets and end the paper with some extensions to other manifolds as well as posing some general problems for the understanding of minimal homeomorphisms of 3-manifolds.
| 2026 | |
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DYNAMICAL SYSTEMS GEOMETRIC TOPOLOGY QUASIGEODESIC FLOWS 3-MANIFOLDS FOLIATIONS ROTATION THEORY MINIMAL HOMEOMORPHISMS |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/54815 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1875693318838419456 |
|---|---|
| author | Gomes, Elena |
| author2 | Martinchich, Santiago Potrie Altieri, Rafael |
| author2_role | author author |
| author_facet | Gomes, Elena Martinchich, Santiago Potrie Altieri, Rafael |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Gomes Elena Martinchich Santiago, Universidad de la República (Uruguay). Ciencias Económicas y Administración Santiago Potrie Altieri Rafael, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. |
| dc.creator.none.fl_str_mv | Gomes, Elena Martinchich, Santiago Potrie Altieri, Rafael |
| dc.date.accessioned.none.fl_str_mv | 2026-05-07T15:35:10Z |
| dc.date.available.none.fl_str_mv | 2026-05-07T15:35:10Z |
| dc.date.issued.none.fl_str_mv | 2026 |
| dc.description.abstract.none.fl_txt_mv | We prove that under some assumptions on how points escape to infinity in the universal cover, homeomorphisms of hyperbolic 3-manifolds are forced to have several invariant sets (in particular, they cannot be minimal). For this, we use some shadowing techniques which, when the homeomorphism has positive speed with respect to a uniform foliation, allow us to obtain strong consequences on the structure of the invariant sets. We discuss also homological rotation sets and end the paper with some extensions to other manifolds as well as posing some general problems for the understanding of minimal homeomorphisms of 3-manifolds. |
| dc.description.es.fl_txt_mv | Publicado también en : Proceedings of the London Mathematical Society, 2026, 132(4). DOI: 10.1112/plms.70139 |
| dc.format.extent.es.fl_str_mv | 33 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Gomes, E, Martinchich, S y Potrie Altieri, R. "Invariant sets for homeomorphisms of hyperbolic 3-manifolds" [Preprint]. Publicado en: Mathematics (Dynamical Systems). 2026 arXiv:2504.03425, feb. 2026, pp. 1-33. DOI: 10.48550/arXiv.2504.03425 |
| dc.identifier.doi.none.fl_str_mv | 10.48550/arXiv.2504.03425 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/54815 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | arXiv |
| dc.relation.none.fl_str_mv | Mathematics (Dynamical Systems), arXiv:2504.03425, feb. 2026, pp. 1-33 |
| 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 | DYNAMICAL SYSTEMS GEOMETRIC TOPOLOGY QUASIGEODESIC FLOWS 3-MANIFOLDS FOLIATIONS ROTATION THEORY MINIMAL HOMEOMORPHISMS |
| dc.title.none.fl_str_mv | Invariant sets for homeomorphisms of hyperbolic 3-manifolds |
| 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 | Publicado también en : Proceedings of the London Mathematical Society, 2026, 132(4). DOI: 10.1112/plms.70139 |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_5af3e5e34669c9d2d0ab23733be60bdb |
| identifier_str_mv | Gomes, E, Martinchich, S y Potrie Altieri, R. "Invariant sets for homeomorphisms of hyperbolic 3-manifolds" [Preprint]. Publicado en: Mathematics (Dynamical Systems). 2026 arXiv:2504.03425, feb. 2026, pp. 1-33. DOI: 10.48550/arXiv.2504.03425 10.48550/arXiv.2504.03425 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/54815 |
| publishDate | 2026 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | karina.camps@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 | Gomes ElenaMartinchich Santiago, Universidad de la República (Uruguay). Ciencias Económicas y Administración SantiagoPotrie Altieri Rafael, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.2026-05-07T15:35:10Z2026-05-07T15:35:10Z2026Gomes, E, Martinchich, S y Potrie Altieri, R. "Invariant sets for homeomorphisms of hyperbolic 3-manifolds" [Preprint]. Publicado en: Mathematics (Dynamical Systems). 2026 arXiv:2504.03425, feb. 2026, pp. 1-33. DOI: 10.48550/arXiv.2504.03425https://hdl.handle.net/20.500.12008/5481510.48550/arXiv.2504.03425Publicado también en : Proceedings of the London Mathematical Society, 2026, 132(4). DOI: 10.1112/plms.70139We prove that under some assumptions on how points escape to infinity in the universal cover, homeomorphisms of hyperbolic 3-manifolds are forced to have several invariant sets (in particular, they cannot be minimal). For this, we use some shadowing techniques which, when the homeomorphism has positive speed with respect to a uniform foliation, allow us to obtain strong consequences on the structure of the invariant sets. We discuss also homological rotation sets and end the paper with some extensions to other manifolds as well as posing some general problems for the understanding of minimal homeomorphisms of 3-manifolds.Submitted by Egaña Lachaga Florencia (florencia.egana@fic.edu.uy) on 2026-05-07T15:22:50Z No. of bitstreams: 2 license_rdf: 27293 bytes, checksum: d62648cf14c1e37917d392ac87012955 (MD5) 2504.03425v2.pdf: 718101 bytes, checksum: acea4eb74b85825035aa1c36b1495355 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2026-05-07T15:30:35Z (GMT) No. of bitstreams: 2 license_rdf: 27293 bytes, checksum: d62648cf14c1e37917d392ac87012955 (MD5) 2504.03425v2.pdf: 718101 bytes, checksum: acea4eb74b85825035aa1c36b1495355 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2026-05-07T15:35:10Z (GMT). No. of bitstreams: 2 license_rdf: 27293 bytes, checksum: d62648cf14c1e37917d392ac87012955 (MD5) 2504.03425v2.pdf: 718101 bytes, checksum: acea4eb74b85825035aa1c36b1495355 (MD5) Previous issue date: 202633 h.application/pdfenengarXivMathematics (Dynamical Systems), arXiv:2504.03425, feb. 2026, pp. 1-33Las 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)DYNAMICAL SYSTEMSGEOMETRIC TOPOLOGYQUASIGEODESIC FLOWS3-MANIFOLDSFOLIATIONSROTATION THEORYMINIMAL HOMEOMORPHISMSInvariant sets for homeomorphisms of hyperbolic 3-manifoldsPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaGomes, ElenaMartinchich, SantiagoPotrie Altieri, RafaelLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/54815/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/54815/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | Invariant sets for homeomorphisms of hyperbolic 3-manifolds Gomes, Elena DYNAMICAL SYSTEMS GEOMETRIC TOPOLOGY QUASIGEODESIC FLOWS 3-MANIFOLDS FOLIATIONS ROTATION THEORY MINIMAL HOMEOMORPHISMS |
| status_str | submittedVersion |
| title | Invariant sets for homeomorphisms of hyperbolic 3-manifolds |
| title_full | Invariant sets for homeomorphisms of hyperbolic 3-manifolds |
| title_fullStr | Invariant sets for homeomorphisms of hyperbolic 3-manifolds |
| title_full_unstemmed | Invariant sets for homeomorphisms of hyperbolic 3-manifolds |
| title_short | Invariant sets for homeomorphisms of hyperbolic 3-manifolds |
| title_sort | Invariant sets for homeomorphisms of hyperbolic 3-manifolds |
| topic | DYNAMICAL SYSTEMS GEOMETRIC TOPOLOGY QUASIGEODESIC FLOWS 3-MANIFOLDS FOLIATIONS ROTATION THEORY MINIMAL HOMEOMORPHISMS |
| url | https://hdl.handle.net/20.500.12008/54815 |
