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Regular version of the site

Article

Topological classification of Morse-Smale diffeomorphisms without heteroclinic intersection

Journal of Mathematical Sciences. 2015. Vol. 208. No. 1. P. 81-91.

We study the class G(Mn)of orientation-preserving Morse–Smale diffeomorfisms on a connected closed smooth manifold Mn of dimension n>3 which is defined by the following condition: for any f∈G(Mn)the invariant manifolds of saddle periodic points have dimension1and(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.