V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, O. V. Pochinka, “On embedding a Morse-Smale diffeomorphism on a 3-manifold in a topological flow”, Mat. Sb., 2012, Volume 203, Number 12,Pages <nobr>81

This article is cited in 17 papers

On embedding a Morse-Smale diffeomorphism on a 3-manifold in a topological flow

V. Z. Grines^a, E. Ya. Gurevich^a, V. S. Medvedev^b, O. V. Pochinka^a

^a N. I. Lobachevski State University of Nizhni Novgorod
^b Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod

Abstract: In this paper, for the case of 3-dimensional manifolds, we solve the Palis problem on finding necessary and sufficient conditions for a Morse-Smale cascade to embed in a topological flow. The set of such cascades is open in the space of all diffeomorphisms, while the set of arbitrary diffeomorphisms that embed in a smooth flow is nowhere dense. Also, we consider a class of diffeomorphisms that embed in a topological flow and prove that a complete topological invariant for this class is similar to the Andronova-Maier scheme and the Peixoto graph.
Bibliography: 26 titles.

Keywords: Morse-Smale diffeomorphism, Morse-Smale cascade, embedding in a flow, dynamical systems on manifolds.

UDC: 517.938

MSC: Primary 37D15; Secondary 37C05, 37C15

Received: 15.12.2011 and 02.05.2012

DOI: 10.4213/sm8094