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arXiv · 1806.03468

On Embedding of Multidimensional Morse-Smale Diffeomorphisms in Topological Flows

Vyacheslav Z. Grines·Elena Y. Gurevich·Olga V. Pochinka
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Abstract

J.~Palis found necessary conditions for a Morse-Smale diffeomorphism on a closed $n$-dimensional manifold $M^n$ to embed into a topological flow and proved that these conditions are also sufficient for $n=2$. For the case $n=3$ a possibility of wild embedding of closures of separatrices of saddles is an additional obstacle for Morse-Smale cascades to embed into topological flows. In this paper we show that there are no such obstructions for Morse-Smale diffeomorphisms without heteroclinic intersection given on the sphere $S^n, \,n\geq 4$, and Palis's conditions again are sufficient for such diffeomorphisms.

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Vyacheslav Z. Grines, Elena Y. Gurevich, Olga V. Pochinka. 2018-06-09. On Embedding of Multidimensional Morse-Smale Diffeomorphisms in Topological Flows. https://arxiv.org/abs/1806.03468

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