Topological entropy of continuous self–maps on a graph

Let G be a graph and f be a continuous self–map on G. We provide sufficient conditions based on the Lefschetz zeta function in order that f has positive topological entropy. Moreover, for the particular graphs: p–flower graph, n-lips graph and (p+r1L1+:::+rsLs)–graph we are able to go further and st...

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Bibliographic Details
Authors: García Guirao, Juan Luis, Llibre Saló, Jaume, Gao, Wei
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2019
Country:España
Institution:Universidad Politécnica de Cartagena(UPCT)
Repository:Repositorio Digital UPCT
OAI Identifier:oai:repositorio.upct.es:10317/8502
Online Access:http://hdl.handle.net/10317/8502
https://link.springer.com/article/10.1007%2Fs40314-019-0969-3
Access Level:Open access
Keyword:Topological graph
Discrete dynamical systems
Lefschetz numbers
Lefschetz zeta function
Periodic point
Period
Topological entropy
Matemática Aplicada
12 Matemáticas
Description
Summary:Let G be a graph and f be a continuous self–map on G. We provide sufficient conditions based on the Lefschetz zeta function in order that f has positive topological entropy. Moreover, for the particular graphs: p–flower graph, n-lips graph and (p+r1L1+:::+rsLs)–graph we are able to go further and state more precise conditions for having positive topological entropy.