Classification of Morse-Smale diffeomorphisms with one-dimensional set of unstable separatrices
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.
orientation-preserving Morse-Smale diffeomorphisms
scientific article; zbMATH DE number 5866955
scientific article