Moscow Mathematical Journal
Volume 19, Issue 4, October–December 2019 pp. 739–760.
On Embedding of Multidimensional Morse–Smale Diffeomorphisms into Topological Flows
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.
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:
Keywords: Morse–Smale dynamical systems, embedding in topological flows, topological classification.
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