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    Necessary and sufficient conditions for topological classification of Morse–Smale cascades on 3-manifolds

    2011, Vol. 7, No. 2, pp.  227-238

    Author(s): Pochinka O. V.

    In this paper class $MS(M^3)$ of Morse–Smale diffeomorphisms (cascades) given on connected closed orientable 3-manifolds are considered. For a diffeomorphism $f \in MS(M^3)$ it is introduced a notion scheme $S_f$, which contains an information on the periodic data of the cascade and a topology of embedding of the sepsrstrices of the saddle points. It is established that necessary and sufficient condition for topological conjugacy of diffeomorphisms $f$, $f’ \in MS(M^3)$ is the equivalence of the schemes $S_f$, $S_f’$.
    Keywords: Morse–Smale diffeomorphism (cascade), topological conjugacy, space orbit
    Citation: Pochinka O. V., Necessary and sufficient conditions for topological classification of Morse–Smale cascades on 3-manifolds, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 2, pp.  227-238
    DOI:10.20537/nd1102003


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