Robust transitivity and domination for endomorphisms displaying critical points
Resumen:
We show that robustly transitive endomorphisms of a closed manifolds must have a non-trivial dominated splitting or be a local diffeomorphism. This allows to get some topological obstructions for the existence of robustly transitive endomorphisms. To obtain the result we must understand the structure of the kernel of the differential and the recurrence to the critical set of the endomorphism after perturbation.
| 2023 | |
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MATHEMATICS - DYNAMICAL SYSTEMS ENDOMORPHISM CRITICAL POINTS DOMINATED SPLITTING ROBUST TRANSITIVITY |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/44886 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522810116964352 |
|---|---|
| author | Lizana Araneda, Cristina |
| author2 | Potrie Altieri, Rafael Pujals, Enrique Ranter, Wagner |
| author2_role | author author author |
| author_facet | Lizana Araneda, Cristina Potrie Altieri, Rafael Pujals, Enrique Ranter, Wagner |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Lizana Araneda Cristina Potrie Altieri Rafael, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. Pujals Enrique Ranter Wagner |
| dc.creator.none.fl_str_mv | Lizana Araneda, Cristina Potrie Altieri, Rafael Pujals, Enrique Ranter, Wagner |
| dc.date.accessioned.none.fl_str_mv | 2024-07-24T12:23:34Z |
| dc.date.available.none.fl_str_mv | 2024-07-24T12:23:34Z |
| dc.date.issued.none.fl_str_mv | 2023 |
| dc.description.abstract.none.fl_txt_mv | We show that robustly transitive endomorphisms of a closed manifolds must have a non-trivial dominated splitting or be a local diffeomorphism. This allows to get some topological obstructions for the existence of robustly transitive endomorphisms. To obtain the result we must understand the structure of the kernel of the differential and the recurrence to the critical set of the endomorphism after perturbation. |
| dc.description.es.fl_txt_mv | Versión permitida preprint. Publicado también en: Ergodic Theory and Dynamical Systems, 2024, 44(2): pp. 594 - 629. DOI: 10.1017/etds.2023.25 |
| dc.format.extent.es.fl_str_mv | 34 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Lizana Araneda, C, Potrie Altieri, R, Pujals, E [y otros]. "Robust transitivity and domination for endomorphisms displaying critical points". [Preprint] Publicado en: Mathematics (Dynamical Systems). arXiv.2106.03291, feb. 2023, pp. 1-34. |
| dc.identifier.doi.none.fl_str_mv | 10.48550/arXiv.2106.03291 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/44886 |
| 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.2106.03291, feb. 2023, pp. 1-34. |
| 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 ENDOMORPHISM CRITICAL POINTS DOMINATED SPLITTING ROBUST TRANSITIVITY |
| dc.title.none.fl_str_mv | Robust transitivity and domination for endomorphisms displaying critical points |
| 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 | Versión permitida preprint. |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_fe7702c67548bb2269e90fbfdf7b870d |
| identifier_str_mv | Lizana Araneda, C, Potrie Altieri, R, Pujals, E [y otros]. "Robust transitivity and domination for endomorphisms displaying critical points". [Preprint] Publicado en: Mathematics (Dynamical Systems). arXiv.2106.03291, feb. 2023, pp. 1-34. 10.48550/arXiv.2106.03291 |
| 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:20.500.12008/44886 |
| publishDate | 2023 |
| 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 | Lizana Araneda CristinaPotrie Altieri Rafael, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Pujals EnriqueRanter Wagner2024-07-24T12:23:34Z2024-07-24T12:23:34Z2023Lizana Araneda, C, Potrie Altieri, R, Pujals, E [y otros]. "Robust transitivity and domination for endomorphisms displaying critical points". [Preprint] Publicado en: Mathematics (Dynamical Systems). arXiv.2106.03291, feb. 2023, pp. 1-34.https://hdl.handle.net/20.500.12008/4488610.48550/arXiv.2106.03291Versión permitida preprint.Publicado también en: Ergodic Theory and Dynamical Systems, 2024, 44(2): pp. 594 - 629. DOI: 10.1017/etds.2023.25We show that robustly transitive endomorphisms of a closed manifolds must have a non-trivial dominated splitting or be a local diffeomorphism. This allows to get some topological obstructions for the existence of robustly transitive endomorphisms. To obtain the result we must understand the structure of the kernel of the differential and the recurrence to the critical set of the endomorphism after perturbation.Submitted by Egaña Florencia (florega@gmail.com) on 2024-07-23T15:17:58Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 2106.03291v4.pdf: 438399 bytes, checksum: c80b923fa9de1311da88d17ad2a02737 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2024-07-24T12:06:48Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 2106.03291v4.pdf: 438399 bytes, checksum: c80b923fa9de1311da88d17ad2a02737 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2024-07-24T12:23:34Z (GMT). No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 2106.03291v4.pdf: 438399 bytes, checksum: c80b923fa9de1311da88d17ad2a02737 (MD5) Previous issue date: 202334 h.application/pdfenengarXivMathematics (Dynamical Systems), arXiv.2106.03291, feb. 2023, pp. 1-34.Las 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 SYSTEMSENDOMORPHISMCRITICAL POINTSDOMINATED SPLITTINGROBUST TRANSITIVITYRobust transitivity and domination for endomorphisms displaying critical pointsPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaLizana Araneda, CristinaPotrie Altieri, RafaelPujals, EnriqueRanter, WagnerLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/44886/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/44886/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | Robust transitivity and domination for endomorphisms displaying critical points Lizana Araneda, Cristina MATHEMATICS - DYNAMICAL SYSTEMS ENDOMORPHISM CRITICAL POINTS DOMINATED SPLITTING ROBUST TRANSITIVITY |
| status_str | submittedVersion |
| title | Robust transitivity and domination for endomorphisms displaying critical points |
| title_full | Robust transitivity and domination for endomorphisms displaying critical points |
| title_fullStr | Robust transitivity and domination for endomorphisms displaying critical points |
| title_full_unstemmed | Robust transitivity and domination for endomorphisms displaying critical points |
| title_short | Robust transitivity and domination for endomorphisms displaying critical points |
| title_sort | Robust transitivity and domination for endomorphisms displaying critical points |
| topic | MATHEMATICS - DYNAMICAL SYSTEMS ENDOMORPHISM CRITICAL POINTS DOMINATED SPLITTING ROBUST TRANSITIVITY |
| url | https://hdl.handle.net/20.500.12008/44886 |
