Topological classification of Morse-Smale diffeomorphisms without heteroclinic intersections
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.
scientific article; zbMATH DE number 6497503
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