The bifurcation set as a topological invariant for one-dimensional dynamics
Resumen:
For a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily small changes of (some of) their endpoints. By assuming a global perspective and focusing on the geometric and topological properties of this collection rather than the surviving sets of individual holes, we obtain a novel topological invariant for one-dimensional dynamics. We provide a detailed description of this invariant in the realm of transitive maps and observe that it carries fundamental dynamical information. In particular, for transitive non-minimal piecewise monotone maps, the bifurcation set encodes the topological entropy and strongly depends on the behavior of the critical points.
| 2021 | |
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One-dimensional dynamics Open systems Topological invariants Bifurcation set/locus |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/34220 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución (CC - By 4.0) |
| _version_ | 1807522793614475264 |
|---|---|
| author | Fuhrmann, Gabriel |
| author2 | Gröger, Maik Passeggi, Alejandro |
| author2_role | author author |
| author_facet | Fuhrmann, Gabriel Gröger, Maik Passeggi, Alejandro |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Fuhrmann Gabriel Gröger Maik Passeggi Alejandro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. |
| dc.creator.none.fl_str_mv | Fuhrmann, Gabriel Gröger, Maik Passeggi, Alejandro |
| dc.date.accessioned.none.fl_str_mv | 2022-10-17T17:37:41Z |
| dc.date.available.none.fl_str_mv | 2022-10-17T17:37:41Z |
| dc.date.issued.none.fl_str_mv | 2021 |
| dc.description.abstract.none.fl_txt_mv | For a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily small changes of (some of) their endpoints. By assuming a global perspective and focusing on the geometric and topological properties of this collection rather than the surviving sets of individual holes, we obtain a novel topological invariant for one-dimensional dynamics. We provide a detailed description of this invariant in the realm of transitive maps and observe that it carries fundamental dynamical information. In particular, for transitive non-minimal piecewise monotone maps, the bifurcation set encodes the topological entropy and strongly depends on the behavior of the critical points. |
| dc.format.extent.es.fl_str_mv | 24 h |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Fuhrmann, G, Gröger, M y Passeggi, A. "The bifurcation set as a topological invariant for one-dimensional dynamics". Nonlinearity. [en línea] 2021, 34(3): 1366–1388. 24 h. DOI: 10.1088/1361-6544/abb78c. |
| dc.identifier.doi.none.fl_str_mv | 10.1088/1361-6544/abb78c |
| dc.identifier.issn.none.fl_str_mv | 1361-6544 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/34220 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | IOP |
| dc.relation.ispartof.es.fl_str_mv | Nonlinearity, 2021, 34(3): 1366–1388. |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución (CC - By 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.es.fl_str_mv | One-dimensional dynamics Open systems Topological invariants Bifurcation set/locus |
| dc.title.none.fl_str_mv | The bifurcation set as a topological invariant for one-dimensional dynamics |
| dc.type.es.fl_str_mv | Artículo |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/article |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| description | For a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily small changes of (some of) their endpoints. By assuming a global perspective and focusing on the geometric and topological properties of this collection rather than the surviving sets of individual holes, we obtain a novel topological invariant for one-dimensional dynamics. We provide a detailed description of this invariant in the realm of transitive maps and observe that it carries fundamental dynamical information. In particular, for transitive non-minimal piecewise monotone maps, the bifurcation set encodes the topological entropy and strongly depends on the behavior of the critical points. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | COLIBRI_4faf92d378150a7da7e31e01866158ed |
| identifier_str_mv | Fuhrmann, G, Gröger, M y Passeggi, A. "The bifurcation set as a topological invariant for one-dimensional dynamics". Nonlinearity. [en línea] 2021, 34(3): 1366–1388. 24 h. DOI: 10.1088/1361-6544/abb78c. 1361-6544 10.1088/1361-6544/abb78c |
| 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:20.500.12008/34220 |
| publishDate | 2021 |
| 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 (CC - By 4.0) |
| spelling | Fuhrmann GabrielGröger MaikPasseggi Alejandro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.2022-10-17T17:37:41Z2022-10-17T17:37:41Z2021Fuhrmann, G, Gröger, M y Passeggi, A. "The bifurcation set as a topological invariant for one-dimensional dynamics". Nonlinearity. [en línea] 2021, 34(3): 1366–1388. 24 h. DOI: 10.1088/1361-6544/abb78c.1361-6544https://hdl.handle.net/20.500.12008/3422010.1088/1361-6544/abb78cFor a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily small changes of (some of) their endpoints. By assuming a global perspective and focusing on the geometric and topological properties of this collection rather than the surviving sets of individual holes, we obtain a novel topological invariant for one-dimensional dynamics. We provide a detailed description of this invariant in the realm of transitive maps and observe that it carries fundamental dynamical information. In particular, for transitive non-minimal piecewise monotone maps, the bifurcation set encodes the topological entropy and strongly depends on the behavior of the critical points.Submitted by Parodi Mónica (mparodi@fcien.edu.uy) on 2022-10-17T17:18:26Z No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) 10108813616544abb78c.pdf: 841767 bytes, checksum: 27ffdc9ae73d6d0f65c7169968409d7c (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2022-10-17T17:32:36Z (GMT) No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) 10108813616544abb78c.pdf: 841767 bytes, checksum: 27ffdc9ae73d6d0f65c7169968409d7c (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2022-10-17T17:37:41Z (GMT). No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) 10108813616544abb78c.pdf: 841767 bytes, checksum: 27ffdc9ae73d6d0f65c7169968409d7c (MD5) Previous issue date: 202124 happlication/pdfenengIOPNonlinearity, 2021, 34(3): 1366–1388.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 (CC - By 4.0)One-dimensional dynamicsOpen systemsTopological invariantsBifurcation set/locusThe bifurcation set as a topological invariant for one-dimensional dynamicsArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaFuhrmann, GabrielGröger, MaikPasseggi, AlejandroLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/34220/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-844http://localhost:8080/xmlui/bitstream/20.500.12008/34220/2/license_urla0ebbeafb9d2ec7cbb19d7137ebc392cMD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | The bifurcation set as a topological invariant for one-dimensional dynamics Fuhrmann, Gabriel One-dimensional dynamics Open systems Topological invariants Bifurcation set/locus |
| status_str | publishedVersion |
| title | The bifurcation set as a topological invariant for one-dimensional dynamics |
| title_full | The bifurcation set as a topological invariant for one-dimensional dynamics |
| title_fullStr | The bifurcation set as a topological invariant for one-dimensional dynamics |
| title_full_unstemmed | The bifurcation set as a topological invariant for one-dimensional dynamics |
| title_short | The bifurcation set as a topological invariant for one-dimensional dynamics |
| title_sort | The bifurcation set as a topological invariant for one-dimensional dynamics |
| topic | One-dimensional dynamics Open systems Topological invariants Bifurcation set/locus |
| url | https://hdl.handle.net/20.500.12008/34220 |
