Topological classification of Morse-Smale diffeomorphisms without heteroclinic intersections
type: Item
instance of: scholarly article
title: Topological classification of Morse-Smale diffeomorphisms without heteroclinic intersections
zbMATH Open document ID: 1378.37044
published in: Journal of Mathematical Sciences (New York)
publication date: 2015-10-23T00:00:00Z
review text: This is a continuation of the papers by \textit{V. Z. Grines} et al. [Proc. Steklov Inst. Math. 261, 59--83 (2008; Zbl 1233.37016); translation from Tr. Mat. Inst. Steklova 261, 61--86 (2008); Proc. Steklov Inst. Math. 270, 57--79 (2010; Zbl 1226.37012); translation from Trudy Mat. Inst. Steklova 270, 62--85 (2010)]. For a connected closed smooth orientable manifold \(M^n\) of dimension \(n\geq 4\), the authors study those orientation-preserving Morse-Smale diffeomorphisms \(G(M^n)\) for which the invariant manifolds of saddle periodic points have dimensions \(1\) and \((n-1)\) and contain no heteroclinic intersections. Two main results are provided. The first one is the determination of the supporting manifolds \(M^n\) by using the relation between the numbers of saddle and node periodic orbits of the diffeomorphisms. The second one is the classification of \(G(M^n)\) under topological conjugacy by using the equivalence of schemes of the diffeomorphisms.
reviewed by: Meirong Zhang
Mathematics Subject Classification ID: 37C15
Mathematics Subject Classification ID: 37D05
zbMATH DE Number: 6497503
zbMATH Keywords: Morse-Smale diffeomorphism
zbMATH Keywords: periodic point
zbMATH Keywords: topological conjugacy
zbMATH Keywords: equivalence of schemes
author: V. Z. Grines
author: E. Ya. Gurevich
author: O. V. Pochinka
MaRDI profile type: Publication
full work available at URL: s10958-015-2425-2
OpenAlex ID: W758584950
cites work: Peixoto graph of Morse-Smale diffeomorphisms on manifolds of dimension greater than three
cites work: Classification of Morse-Smale diffeomorphisms with one-dimensional set of unstable separatrices
cites work: Morse-Smale cascades on 3-manifolds
cites work: On Topological Classification of Morse–Smale Diffeomorphisms
cites work: On the simple isotopy class of a source-sink diffeomorphism on the 3-sphere
cites work: Q4337982
cites work: Q3883164
cites work: Q3594455
cites work: Morse inequalities for a dynamical system
cites work: n-Frames in Euclidean k-Space
cites work: Locally flat imbeddings of topological manifolds
cites work: Three-manifolds admitting Morse-Smale diffeomorphisms without heteroclinic curves.
cites work: Q3736463
DOI: 10.1007/S10958-015-2425-2
description: scientific article; zbMATH DE number 6497503