TOPOLOGICAL ENTROPY AND PERIODS OF SELF MAPS ON COMPACT MANIFOLDS

被引：0

作者：

Garcia Guirao, Juan Luis ^{[1
]}

Llibre, Jaume ^{[2
]}

机构：

[1] Univ Politecn Cartagena, Hosp Marina, Dept Math Aplicada & Estadist, Cartagena 30203, Region De Murci, Spain

[2] Univ Autonoma Barcelona, Dept Math, E-08193 Barcelona, Catalonia, Spain

来源：

HOUSTON JOURNAL OF MATHEMATICS | 2017年 / 43卷 / 04期

关键词：

Compact manifold; topological entropy; discrete dynamical systems; Lefschetz numbers; Lefschetz zeta function; periodic point;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 C-infinity, and (2) f has infinitely many periodic points when f is C-1 and f(M) subset of Int(M). Moreover, for the particular manifolds S-n, S-n x S-m CPn and HPn we improve the previous sufficient conditions.

引用

页码：1337 / 1347

页数：11

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