Topological entropy and periods of self-maps on compact manifolds

Juan Luis García Guirao; Jaume Llibre

Topological entropy and periods of self-maps on compact manifolds

Juan Luis García Guirao, Jaume Llibre

Department of Mathematics

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

3 Citations (Scopus)

Abstract

© 2017 University of Houston. Let (M; f) be a discrete dynamical system induced by a self-map f defined on a smooth compact connected n-dimensional manifold M. We provide sufficient conditions in terms of the Lefschetz zeta function in order that: (1) f has positive topological entropy when f is C1, and (2) f has infinitely many periodic points when f is C1 and f(M) Int(M). Moreover, for the particular manifolds Sn, Sn× Sm, CPn and HPn we improve the previous sufficient conditions.

Original language	English
Pages (from-to)	1337-1347
Journal	Houston Journal of Mathematics
Volume	43
Issue number	4
Publication status	Published - 1 Jan 2017

Keywords

Compact manifold
Discrete dynamical systems
Lefschetz numbers
Lefschetz zeta function
Periodic point.
Topological entropy

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title = "Topological entropy and periods of self-maps on compact manifolds",

abstract = "{\textcopyright} 2017 University of Houston. Let (M; f) be a discrete dynamical system induced by a self-map f defined on a smooth compact connected n-dimensional manifold M. We provide sufficient conditions in terms of the Lefschetz zeta function in order that: (1) f has positive topological entropy when f is C1, and (2) f has infinitely many periodic points when f is C1 and f(M) Int(M). Moreover, for the particular manifolds Sn, Sn× Sm, CPn and HPn we improve the previous sufficient conditions.",

keywords = "Compact manifold, Discrete dynamical systems, Lefschetz numbers, Lefschetz zeta function, Periodic point., Topological entropy",

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

year = "2017",

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T1 - Topological entropy and periods of self-maps on compact manifolds

AU - Guirao, Juan Luis García

AU - Llibre, Jaume

PY - 2017/1/1

Y1 - 2017/1/1

N2 - © 2017 University of Houston. Let (M; f) be a discrete dynamical system induced by a self-map f defined on a smooth compact connected n-dimensional manifold M. We provide sufficient conditions in terms of the Lefschetz zeta function in order that: (1) f has positive topological entropy when f is C1, and (2) f has infinitely many periodic points when f is C1 and f(M) Int(M). Moreover, for the particular manifolds Sn, Sn× Sm, CPn and HPn we improve the previous sufficient conditions.

AB - © 2017 University of Houston. Let (M; f) be a discrete dynamical system induced by a self-map f defined on a smooth compact connected n-dimensional manifold M. We provide sufficient conditions in terms of the Lefschetz zeta function in order that: (1) f has positive topological entropy when f is C1, and (2) f has infinitely many periodic points when f is C1 and f(M) Int(M). Moreover, for the particular manifolds Sn, Sn× Sm, CPn and HPn we improve the previous sufficient conditions.

KW - Compact manifold

KW - Discrete dynamical systems

KW - Lefschetz numbers

KW - Lefschetz zeta function

KW - Periodic point.

KW - Topological entropy

M3 - Article

VL - 43

SP - 1337

EP - 1347

JO - Houston Journal of Mathematics

JF - Houston Journal of Mathematics

SN - 0362-1588

IS - 4

ER -