Topological Classification of Morse–Smale Diffeomorphisms Without Heteroclinic Intersections

被引：0

作者：

Grines V.Z. ^{[1
]}

Gurevich E.A. ^{[2
]}

Pochinka O.V. ^{[2
]}

机构：

[1] National Research University Higher School of Economics, Lobachevsky State University of Nizhny Novgorod, 23, Gagarina pr, Nizhny Novgorod

[2] National Research University Higher School of Economics, 25/12, Bol’shaya Pechorskaya St, Nizhny Novgorod

来源：

Journal of Mathematical Sciences | 2015年 / 208卷 / 1期

基金：

俄罗斯基础研究基金会;

关键词：

Manifold; Saddle Point; Vector Bundle; Periodic Point; Invariant Manifold;

D O I：

10.1007/s10958-015-2425-2

中图分类号：

学科分类号：

摘要：

We study the class G(Mn) of orientation-preserving Morse–Smale diffeomorfisms on a connected closed smooth manifold Mn of dimension n ≥ 4 which is defined by the following condition: for any f ∊ G(Mn) the invariant manifolds of saddle periodic points have dimension 1 and (n − 1) and contain no heteroclinic intersections. For diffeomorfisms in G(Mn) we establish the topoligical type of the supporting manifold which is determined by the relation between the numbers of saddle and node periodic orbits and obtain necessary and sufficient conditions for topological conjugacy. Bibliography: 14 titles. © 2015, Springer Science+Business Media New York.

引用

页码：81 / 90

页数：9

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