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Russian Mathematical Surveys, 2013, Volume 68, Issue 1, Pages 117–173
DOI: https://doi.org/10.1070/RM2013v068n01ABEH004823 (Mi rm9489) 		 
This article is cited in 21 scientific papers (total in 21 papers)

Morse–Smale cascades on 3-manifolds

V. Z. Grines, O. V. Pochinka

Nizhnii Novgorod State University
English version PDF (1393 kB) Citations (21)
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DOI: https://doi.org/10.1070/RM2013v068n01ABEH004823
Abstract: This is a survey of recent (from 2000) results obtained by the authors in collaboration with Russian and foreign colleagues. The major theme of our investigations involves Morse–Smale cascades on orientable 3-manifolds and includes a complete topological classification of them, a determination of the interconnection between their dynamics and the topology of the ambient manifold, a criterion for embeddability in a topological flow, and necessary and sufficient conditions for such cascades to have an energy function.
Bibliography: 76 titles.
Keywords: Morse–Smale diffeomorphism, topological classification, embedding in a flow, energy function.
Funding agency Grant number
Russian Foundation for Basic Research 12-01-00672
11-01-12056-офи-м
Ministry of Education and Science of the Russian Federation 11.G34.31.0039
1.1907.2011
Received: 09.06.2012
Russian version:
Uspekhi Matematicheskikh Nauk, 2013, Volume 68, Issue 1(409), Pages 129–188
DOI: https://doi.org/10.4213/rm9489
Bibliographic databases:
Document Type: Article
UDC: 517.938
MSC: Primary 37D15; Secondary 37C05, 37C15, 37E30, 37C29, 37B25, 57M30
Language: English
Original paper language: Russian
Citation: V. Z. Grines, O. V. Pochinka, “Morse–Smale cascades on 3-manifolds”, Uspekhi Mat. Nauk, 68:1(409) (2013), 129–188; Russian Math. Surveys, 68:1 (2013), 117–173
Citation in format AMSBIB
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    • This publication is cited in the following 21 articles:
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    References:83
    First page:37
     
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