Classification of Morse-Smale diffeomorphisms with one-dimensional set of unstable separatrices
type: Item
instance of: scholarly article
title: Classification of Morse-Smale diffeomorphisms with one-dimensional set of unstable separatrices
zbMATH Open document ID: 1226.37012
DOI: 10.1134/S0081543810030053
author: E. Ya. Gurevich
author: Vladislav S. Medvedev
author: V. Z. Grines
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2011-03-17T00:00:00Z
review text: As a continuation of [the authors, ``The Peixoto graph of Morse-Smale diffeomorphisms on manifolds of dimension greater than three'', Tr. Mat. Inst. Steklova 261, 61--86 (2008); translation in Proc. Steklov Inst. Math. 261, 59--83 (2008)] this article is devoted to the topological classification of Morse-Smale diffeomorphisms defined on a closed orientable manifold \(M^n\) of dimension \(n>3\). The authors consider the set \(G_1(M^n)\) of orientation-preserving Morse-Smale diffeomorphisms of \(M^n\) for which the set of unstable separatrices is one-dimensional and does not contain heteroclinic intersections. It is proved that the Peixoto graph, equipped with an automorphism, is a complete topological invariant for diffeomorphisms of class \(G_1(M^n)\), and a standard representative for any class of topologically conjugate diffeomorphisms is constructed.
reviewed by: Irina V. Konopleva
Mathematics Subject Classification ID: 37D15
Mathematics Subject Classification ID: 37C15
Mathematics Subject Classification ID: 37C29
Mathematics Subject Classification ID: 37C05
zbMATH DE Number: 5866955
zbMATH Keywords: orientation-preserving Morse-Smale diffeomorphisms
zbMATH Keywords: unstable separatrices
zbMATH Keywords: heteroclinic intersections
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5866955