THERE ARE NO PROPER TOPOLOGICAL HYPERBOLIC HOMOCLINIC CLASSES FOR AREA-PRESERVING MAPS

被引：1

作者：

Bessa, Mario ^{[1
]}

Torres, Maria Joana ^{[2
,3
]}

机构：

[1] Univ Beira Interior, Dept Matemat, Rua Marques dAvila & Bolama, P-6201001 Covilha, Portugal

[2] Univ Minho, CMAT, Campus Gualtar, P-4700057 Braga, Portugal

[3] Univ Minho, Dept Matemat & Aplicacoes, Campus Gualtar, P-4700057 Braga, Portugal

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2020年 / 63卷 / 01期

关键词：

shadowing; expansiveness; topological dynamics; homoclinic classes;

D O I：

10.1017/S0013091519000282

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We begin by defining a homoclinic class for homeomorphisms. Then we prove that if a topological homoclinic class Lambda associated with an area-preserving homeomorphism f on a surface M is topologically hyperbolic (i.e. has the shadowing and expansiveness properties), then Lambda = M and f is an Anosov homeomorphism.

引用

页码：217 / 228

页数：12

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