Moscow Mathematical Journal

Volume 19, Issue 4, October–December 2019  pp. 739–760.

On Embedding of Multidimensional Morse–Smale Diffeomorphisms into Topological Flows

Authors:  V. Grines (1), E. Gurevich (1), and O. Pochinka (1)
Author institution:(1) National Research University Higher School of Economics Nizhnii Novgorod, B. Pechorskaya str., 25, 224

Summary:

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 conditions again are sufficient for such diffeomorphisms.

2010 Math. Subj. Class. 37D15.

Keywords: Morse–Smale dynamical systems, embedding in topological flows, topological classification.