Periods, Lefschetz numbers and entropy for a class of maps on a bouquet of circles

Jaume Llibre; Michael Todd

doi:10.1080/10236190500331230

Periods, Lefschetz numbers and entropy for a class of maps on a bouquet of circles

Jaume Llibre^*, Michael Todd

^*Corresponding author for this work

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider some smooth maps on a bouquet of circles. For these maps we can compute the number of fixed points, the existence of periodic points and an exact formula for topological entropy. We use Lefschetz fixed point theory and actions of our maps on both the fundamental group and the first homology group.

Original language	English
Pages (from-to)	1049-1069
Number of pages	21
Journal	Journal of Difference Equations and Applications
Volume	11
Issue number	12
DOIs	https://doi.org/10.1080/10236190500331230
Publication status	Published - Oct 2005

Keywords

Graph maps
Lefschetz numbers
Periodic points
Topological entropy

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10.1080/10236190500331230

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abstract = "We consider some smooth maps on a bouquet of circles. For these maps we can compute the number of fixed points, the existence of periodic points and an exact formula for topological entropy. We use Lefschetz fixed point theory and actions of our maps on both the fundamental group and the first homology group.",

keywords = "Graph maps, Lefschetz numbers, Periodic points, Topological entropy",

author = "Jaume Llibre and Michael Todd",

note = "Funding Information: The first author was partially supported by a MCYT grant BFM2002-04236-C02-02 and by a CIRIT grant number 2001SGR 00173, the second one by a Marie Curie Fellowship number HPMT-CT-2001-00247.",

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AU - Todd, Michael

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N2 - We consider some smooth maps on a bouquet of circles. For these maps we can compute the number of fixed points, the existence of periodic points and an exact formula for topological entropy. We use Lefschetz fixed point theory and actions of our maps on both the fundamental group and the first homology group.

AB - We consider some smooth maps on a bouquet of circles. For these maps we can compute the number of fixed points, the existence of periodic points and an exact formula for topological entropy. We use Lefschetz fixed point theory and actions of our maps on both the fundamental group and the first homology group.

KW - Graph maps

KW - Lefschetz numbers

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KW - Topological entropy

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ER -

Periods, Lefschetz numbers and entropy for a class of maps on a bouquet of circles

Abstract

Keywords

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