Vector Fields with the Asymptotic Orbital Pseudo-orbit Tracing Property

被引：3

作者：

Lee, Manseob ^{[1
]}

Park, Junmi ^{[2
]}

机构：

[1] Mokwon Univ, Dept Math, Daejeon 35349, South Korea

[2] Chungnam Natl Univ, Dept Math, Daejeon 34134, South Korea

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2020年 / 19卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

Pseudo-orbit tracing; Limit pseudo-orbit tracing; Asymptotic orbital pseudo-orbit tracing; Chain transitive; Generic; Anosov; SHADOWING PROPERTY; DYNAMICAL-SYSTEMS; FLOWS; HYPERBOLICITY; TRANSITIVITY; STABILITY; SPECIFICATION; SETS;

D O I：

10.1007/s12346-020-00388-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce the notion of the asymptotic orbital pseudo-orbit tracing property for a vector field X of a compact smooth manifold M. We show that if a vector field X has the C1 robust asymptotic orbital pseudo-orbit tracing property, then it is Anosov, and if a C1 generic vector field X has the asymptotic orbital pseudo-orbit tracing property, then it is Anosov. Moreover, we also show our results for divergencefree vector fields and Hamiltonian systems.

引用

页数：16

共 33 条

[1] ON VARIOUS TYPES OF SHADOWING FOR GEOMETRIC LORENZ FLOWS [J].