Topological entropy and periods of graph maps

Jaume Llibre; Radu Saghin

doi:10.1080/10236198.2011.561202

Topological entropy and periods of graph maps

Jaume Llibre, Radu Saghin

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

3 Scopus citations

Abstract

We give a complete description of the set of periods of continuous self-maps on graphs which have zero topological entropy and have all their branching points fixed. As a corollary, we get a criterion for positive topological entropy for continuous self-maps on graphs. We also prove that the results are optimal.

Original language	English
Pages (from-to)	589-598
Number of pages	10
Journal	Journal of Difference Equations and Applications
Volume	18
Issue number	4
DOIs	https://doi.org/10.1080/10236198.2011.561202
State	Published - Apr 2012
Externally published	Yes

Keywords

graph maps
periodic points
periods
topological entropy

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10.1080/10236198.2011.561202

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title = "Topological entropy and periods of graph maps",

abstract = "We give a complete description of the set of periods of continuous self-maps on graphs which have zero topological entropy and have all their branching points fixed. As a corollary, we get a criterion for positive topological entropy for continuous self-maps on graphs. We also prove that the results are optimal.",

keywords = "graph maps, periodic points, periods, topological entropy",

author = "Jaume Llibre and Radu Saghin",

note = "Funding Information: The first author was partially supported by MCI/FEDER grant number MTM 2008-03437, by CICYT grant number 2009SGR410 and by ICREA Academia. The second author was supported by Marie Curie IEF grant number 234559, and would like to thank CRM Barcelona for their hospitality. We would also like to thank the referees for their useful comments and suggestions.",

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AU - Llibre, Jaume

AU - Saghin, Radu

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PY - 2012/4

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N2 - We give a complete description of the set of periods of continuous self-maps on graphs which have zero topological entropy and have all their branching points fixed. As a corollary, we get a criterion for positive topological entropy for continuous self-maps on graphs. We also prove that the results are optimal.

AB - We give a complete description of the set of periods of continuous self-maps on graphs which have zero topological entropy and have all their branching points fixed. As a corollary, we get a criterion for positive topological entropy for continuous self-maps on graphs. We also prove that the results are optimal.

KW - graph maps

KW - periodic points

KW - periods

KW - topological entropy

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U2 - 10.1080/10236198.2011.561202

DO - 10.1080/10236198.2011.561202

M3 - Article

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JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

IS - 4

ER -

Topological entropy and periods of graph maps

Abstract

Keywords

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