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Mat. Sb., 2012, Volume 203, Number 12, Pages 81–104 (Mi msb8094)  

This article is cited in 5 scientific papers (total in 5 papers)

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

V. Z. Grinesa, E. Ya. Gurevicha, V. S. Medvedevb, O. V. Pochinkaa

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.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8094

Full text: PDF file (812 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2012, 203:12, 1761–1784

Bibliographic databases:

UDC: 517.938
MSC: Primary 37D15; Secondary 37C05, 37C15
Received: 15.12.2011 and 02.05.2012

Citation: 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., 203:12 (2012), 81–104; Sb. Math., 203:12 (2012), 1761–1784

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. Z. Grines, O. V. Pochinka, “Morse–Smale cascades on 3-manifolds”, Russian Math. Surveys, 68:1 (2013), 117–173  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. V. Z. Grines, E. Ya. Gurevich, O. V. Pochinka, “On embedding Morse–Smale diffeomorphisms on the sphere in topological flows”, Russian Math. Surveys, 71:6 (2016), 1146–1148  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Sergey M. Saulin, Dmitry V. Treschev, “On the Inclusion of a Map Into a Flow”, Regul. Chaotic Dyn., 21:5 (2016), 538–547  mathnet  crossref  mathscinet  zmath  elib
    4. I. A. Dynnikov, A. A. Glutsyuk, A. E. Mironov, I. A. Taimanov, A. Yu. Vesnin, “The conference “Dynamics in Siberia”, Novosibirsk, February 29–March 4, 2016”, Sib. elektron. matem. izv., 14 (2017), A.7–A.30  mathnet  crossref  mathscinet  isi
    5. V. Z. Grines, E. Ya. Gurevich, E. V. Zhuzhoma, O. V. Pochinka, “Classification of Morse–Smale systems and topological structure of the underlying manifolds”, Russian Math. Surveys, 74:1 (2019), 37–110  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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