Topological entropy of continuous self-maps on closed surfaces

Juan Luis García Guirao; Jaume Llibre; Wei Gao

doi:https://doi.org/10.1080/10236198.2019.1710141

Topological entropy of continuous self-maps on closed surfaces

Juan Luis García Guirao^*, Jaume Llibre, Wei Gao

^*Corresponding author for this work

Department of Mathematics

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

Abstract

The objective of this work is to present sufficient conditions for having positive topological entropy for continuous self-maps defined on a closed surface by using the action of this map on the homological groups of the closed surface.

Original language	English
Pages (from-to)	203-208
Number of pages	6
Journal	Journal of difference equations and applications
Volume	26
Issue number	2
DOIs	https://doi.org/10.1080/10236198.2019.1710141
Publication status	Published - 1 Feb 2020

Keywords

Closed surface
Lefschetz fixed point theory
continuous self-map
periodic point
set of periods

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https://doi.org/10.1080/10236198.2019.1710141

https://ddd.uab.cat/record/221330

Cite this

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title = "Topological entropy of continuous self-maps on closed surfaces",

abstract = "The objective of this work is to present sufficient conditions for having positive topological entropy for continuous self-maps defined on a closed surface by using the action of this map on the homological groups of the closed surface.",

keywords = "Closed surface, Lefschetz fixed point theory, continuous self-map, periodic point, set of periods",

author = "{Garc{\'i}a Guirao}, {Juan Luis} and Jaume Llibre and Wei Gao",

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AU - García Guirao, Juan Luis

AU - Llibre, Jaume

AU - Gao, Wei

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N2 - The objective of this work is to present sufficient conditions for having positive topological entropy for continuous self-maps defined on a closed surface by using the action of this map on the homological groups of the closed surface.

AB - The objective of this work is to present sufficient conditions for having positive topological entropy for continuous self-maps defined on a closed surface by using the action of this map on the homological groups of the closed surface.

KW - Closed surface

KW - Lefschetz fixed point theory

KW - continuous self-map

KW - periodic point

KW - set of periods

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JF - Journal of difference equations and applications

IS - 2

ER -

Topological entropy of continuous self-maps on closed surfaces

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