On Embedding of Multidimensional Morse–Smale Diffeomorphisms into Topological Flows

IF 0.6 4区数学 Q3 MATHEMATICS

Moscow Mathematical Journal Pub Date : 2018-06-09 DOI:10.17323/1609-4514-2019-19-4-739-760

V. Grines, E. Gurevich, O. Pochinka

引用次数: 6

Abstract

J.~Palis found necessary conditions for a Morse-Smale diffeomorphism on a closed $n$-dimensional manifold $M^n$ to embed into a topological flow and proved that these conditions are also sufficient for $n=2$. For the case $n=3$ a possibility of wild embedding of closures of separatrices of saddles is an additional obstacle for Morse-Smale cascades to embed into topological flows. In this paper we show that there are no such obstructions for Morse-Smale diffeomorphisms without heteroclinic intersection given on the sphere $S^n, \,n\geq 4$, and Palis's conditions again are sufficient for such diffeomorphisms.

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多维Morse–Smale差同态在拓扑流中的嵌入

J.~Palis发现了闭$n$维流形$M^n$上Morse Smale微分同胚嵌入拓扑流的必要条件，并证明了这些条件对于$n=2$也是充分的。对于$n=3$的情况，鞍形分离基的闭包的野生嵌入的可能性是Morse Smale级联嵌入拓扑流的额外障碍。在本文中，我们证明了在球面$S^n，\，n\geq4$上不存在异宿交的Morse Smale微分同胚不存在这样的障碍，并且Palis条件对于这样的微分同胚也是充分的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Moscow Mathematical Journal 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Moscow Mathematical Journal (MMJ) is an international quarterly published (paper and electronic) by the Independent University of Moscow and the department of mathematics of the Higher School of Economics, and distributed by the American Mathematical Society. MMJ presents highest quality research and research-expository papers in mathematics from all over the world. Its purpose is to bring together different branches of our science and to achieve the broadest possible outlook on mathematics, characteristic of the Moscow mathematical school in general and of the Independent University of Moscow in particular. An important specific trait of the journal is that it especially encourages research-expository papers, which must contain new important results and include detailed introductions, placing the achievements in the context of other studies and explaining the motivation behind the research. The aim is to make the articles — at least the formulation of the main results and their significance — understandable to a wide mathematical audience rather than to a narrow class of specialists.