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Sbornik: Mathematics, 2012, Volume 203, Issue 12, Pages 1761–1784
DOI: https://doi.org/10.1070/SM2012v203n12ABEH004286 (Mi sm8094) 		 
This article is cited in 17 scientific papers (total in 17 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
English version PDF (552 kB) Citations (17)
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DOI: https://doi.org/10.1070/SM2012v203n12ABEH004286
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.
Received: 15.12.2011 and 02.05.2012
Russian version:
Matematicheskii Sbornik, 2012, Volume 203, Number 12, Pages 81–104
DOI: https://doi.org/10.4213/sm8094
Bibliographic databases:
Document Type: Article
UDC: 517.938
MSC: Primary 37D15; Secondary 37C05, 37C15
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:70
    First page:19
     
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