Vector fields with the oriented shadowing property

被引：16

作者：

Pilyugin, Sergei Yu. ^{[2
]}

Tikhomirov, Sergey B. ^{[1
]}

机构：

[1] Natl Taiwan Univ, Dept Math, Taipei 106, Taiwan

[2] St Petersburg State Univ, Fac Math & Mech, St Petersburg 198504, Russia

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2010年 / 248卷 / 06期

关键词：

Vector fields; Oriented shadowing; Structural stability; ORBIT-TRACING-PROPERTY; ONE-PARAMETER FLOWS; STABILITY;

D O I：

10.1016/j.jde.2009.09.024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a description of the C-1-interior (Int(1) (OrientSh)) of the set of smooth vector fields on a smooth closed manifold that have the oriented shadowing property. A special class B of vector fields that are not structurally stable is introduced. It is shown that the set Int(1) (OrientSh\B) coincides with the set of structurally stable vector fields. An example of a field of the class B belonging to Int(1) (OrientSh) is given. Bibliography: 18 titles. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：1345 / 1375

页数：31

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