Topological entropy of continuous self–maps on a graph
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The second author is partially supported by the Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación grants MTM-2016-77278-P (FEDER) and MDM-2014-0445, the Agència de Gestió d’Ajuts Universitaris i de Recerca grant 2017SGR1617, and the H2020 European Research Council grant MSCA-RISE-2017-777911.Fecha de publicación
2019Editorial
Springer Science and Business MediaCita bibliográfica
Guirao, Juan & Llibre, Jaume & Gao, Wei. (2019). Topological entropy of continuous self-maps on a graph. Computational and Applied Mathematics. 38. 10.1007/s40314-019-0969-3Palabras clave
Topological graphDiscrete dynamical systems
Lefschetz numbers
Lefschetz zeta function
Periodic point
Period
Topological entropy
Resumen
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.
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