MORSE-SMALE SYSTEMS AND HORSESHOES FOR THREE DIMENSIONAL SINGULAR FLOWS

被引：27

作者：

Gan, Shaobo ^{[1
]}

Yang, Dawei ^{[2
]}

机构：

[1] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China

[2] Soochow Univ, Sch Math Sci, Suzhou 215006, Peoples R China

来源：

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE | 2018年 / 51卷 / 01期

关键词：

HOMOCLINIC TANGENCIES; GLOBAL PERSPECTIVE; TRANSITIVE SETS; C-1; STABILITY; HYPERBOLICITY; CONJECTURE; DICHOTOMY; DYNAMICS;

D O I：

10.24033/asens.2351

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that every three-dimensional vector field can be C-1 accumulated by Morse-Smale ones, or by ones with a transverse homoclinic intersection of some hyperbolic periodic orbit. In contrast to the case of diffeomorphisms [14], the main difficulty here is that we need to deal with singularities. We also make progress on another conjecture related to Palis in this paper.

引用

页码：39 / 112

页数：74

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