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Regular version of the site

Article

On Embedding of Multidimensional Morse-Smale Diffeomorphisms into Topological Flows

Moscow Mathematical Journal. 2019. Vol. 19. No. 4. P. 739-760.

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.