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Romero Ruiz del Portal, Francisco and Graff, Grzegorz and Nowak-Przygodzki, Piotr
(2011)
*Local fixed point indices of iterations of planar maps.*
Journal of Dynamics and Differential Equations, 23
(1).
pp. 213-223.
ISSN 1040-7294

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Official URL: http://www.springerlink.com/openurl.asp?genre=journalissn=1040-7294

## 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.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Fixed point index; Conley index, Nielsen number; Periodic points; Iterations |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 13994 |

Deposited On: | 07 Dec 2011 09:12 |

Last Modified: | 12 Dec 2018 15:13 |

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