On Morse--Smale Diffeomorphisms with Four Periodic Points on Closed Orientable Manifolds |
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| Authors: | Grines V Z Zhuzhoma E V Medvedev V S |
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| Institution: | (1) Nizhnii Novgorod State Agricultural Academy, Russia;(2) Nizhnii Novgorod State Technical University, Russia;(3) Institute for Applied Mathematics and Cybernetics, Nizhnii Novgorod State Technical University, Russia |
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| Abstract: | We study Morse--Smale diffeomorphisms of n-manifolds with four periodic points which are the only periodic points. We prove that for n= 3 these diffeomorphisms are gradient-like and define a class of diffeomorphisms inevitably possessing a nonclosed heteroclinic curve. For n  4, we construct a complete conjugacy invariant in the class of diffeomorphisms with a single saddle of codimension one. |
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| Keywords: | Morse--Smale diffeomorphism gradient-like diffeomorphism nonwandering point source sink saddle heteroclinic curve |
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