On shadowing and hyperbolicity for geodesic flows on surfaces

被引：4

作者：

Bessa, Mario ^{[1
]}

Dias, Joao Lopes ^{[2
,3
]}

Torres, Maria Joana ^{[4
,5
]}

机构：

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

[2] Univ Lisbon, Dept Matemat, ISEG, Rua Quelhas 6, P-1200781 Lisbon, Portugal

[3] Univ Lisbon, CEMAPRE, ISEG, Rua Quelhas 6, P-1200781 Lisbon, Portugal

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

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

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 155卷

关键词：

Geodesic flow; Hyperbolic sets; Shadowing; Specification; POSITIVE TOPOLOGICAL-ENTROPY; LEMMA;

D O I：

10.1016/j.na.2017.02.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the geodesic flow on closed surfaces displays a hyperbolic set if the shadowing property holds C-2-robustly on the metric. Similar results are obtained when considering even feeble properties like the weak shadowing and the specification properties. Despite the Hamiltonian nature of the geodesic flow, the arguments in the present paper differ completely from those used in Bessa et al. (2013) for Hamiltonian systems. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：250 / 263

页数：14

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