CONTINUUM-WISE EXPANSIVENESS FOR C1 GENERIC VECTOR FIELDS

被引：0

作者：

Lee, Manseob ^{[1
]}

机构：

[1] Mokwon Univ, Dept Mkt Big Data, Daejeon 35349, South Korea

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2023年 / 60卷 / 05期

关键词：

Expansive; continuum-wise expansive; Axiom A; homoclinic class; hyperbolic; generic; HOMOCLINIC CLASSES; PERIODIC-ORBITS; HYPERBOLICITY; FLOWS;

D O I：

10.4134/JKMS.j220359

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is shown that every continuum-wise expansive C-1 generic vector field X on a compact connected smooth manifold M satisfies Axiom A and has no cycles, and every continuum-wise expansive homoclinic class of a C-1 generic vector field X on a compact connected smooth manifold M is hyperbolic. Moreover, every continuum-wise expansive C-1 generic divergence-free vector field X on a compact connected smooth manifold M is Anosov.

引用

页码：987 / 998

页数：12

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