Local fixed point indices of iterations of planar maps
| dc.contributor.author | Romero Ruiz del Portal, Francisco | |
| dc.contributor.author | Graff, Grzegorz | |
| dc.contributor.author | Nowak-Przygodzki, Piotr | |
| dc.date.accessioned | 2023-06-20T00:07:15Z | |
| dc.date.available | 2023-06-20T00:07:15Z | |
| dc.date.issued | 2011 | |
| dc.description.abstract | Let f : U →R2 be a continuous map, where U is an open subset of R2. We consider a fixed point p of f which is neither a sink nor a source and such that p is an isolated invariant set. Under these assumption we prove, using Conley index methods and Nielsen theory, that the sequence of fixed point indices of iterations ind(fn, p) n=1 is periodic,bounded by 1, and has infinitely many non-positive terms, which is a generalization of Le Calvez and Yoccoz theorem [Annals of Math., 146 (1997), 241-293] onto the class of non-injective maps. We apply our result to study the dynamics of continuous maps on 2-dimensional sphere. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | MSHE | |
| dc.description.sponsorship | MICINN | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/13994 | |
| dc.identifier.doi | 10.1007/s10884-011-9204-7 | |
| dc.identifier.issn | 1040-7294 | |
| dc.identifier.officialurl | http://www.springerlink.com/openurl.asp?genre=journalissn=1040-7294 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/42017 | |
| dc.issue.number | 1 | |
| dc.journal.title | Journal of Dynamics and Differential Equations | |
| dc.language.iso | eng | |
| dc.page.final | 223 | |
| dc.page.initial | 213 | |
| dc.publisher | Springer | |
| dc.relation.projectID | N N201 373236 | |
| dc.relation.projectID | MTM2006-0825. | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 515.1 | |
| dc.subject.keyword | Fixed point index | |
| dc.subject.keyword | Conley index | |
| dc.subject.keyword | Nielsen number | |
| dc.subject.keyword | Periodic points | |
| dc.subject.keyword | Iterations | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Local fixed point indices of iterations of planar maps | |
| dc.type | journal article | |
| dc.volume.number | 23 | |
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| dspace.entity.type | Publication |
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