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Sbornik: Mathematics, 2014, Volume 205, Issue 10, Pages 1387–1412
DOI: https://doi.org/10.1070/SM2014v205n10ABEH004423 (Mi sm8328) 		 
This article is cited in 17 scientific papers (total in 17 papers)

A three-colour graph as a complete topological invariant for gradient-like diffeomorphisms of surfaces

V. Z. Grinesa, S. H. Kapkaevab, O. V. Pochinkaa

a N. I. Lobachevski State University of Nizhni Novgorod
b Ogarev Mordovia State University, Saransk
English version PDF (779 kB) Citations (17)
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DOI: https://doi.org/10.1070/SM2014v205n10ABEH004423
Abstract: In a paper of Oshemkov and Sharko, three-colour graphs were used to make the topological equivalence of Morse-Smale flows on surfaces obtained by Peixoto more precise. In the present paper, in the language of three-colour graphs equipped with automorphisms, we obtain a complete (including realization) topological classification of gradient-like cascades on surfaces.
Bibliography: 25 titles.
Keywords: Morse-Smale diffeomorphism, gradient-like diffeomorphism, three-colour graph, topological classification.
Funding agency Grant number
Russian Foundation for Basic Research 12-01-00672
13-01-12452-офи-м
Received: 15.01.2014
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 10, Pages 19–46
DOI: https://doi.org/10.4213/sm8328
Bibliographic databases:
Document Type: Article
UDC: 517.938
MSC: Primary 37D15; Secondary 37C05, 37C15, 37E30
Language: English
Original paper language: Russian
Citation: V. Z. Grines, S. H. Kapkaeva, O. V. Pochinka, “A three-colour graph as a complete topological invariant for gradient-like diffeomorphisms of surfaces”, Mat. Sb., 205:10 (2014), 19–46; Sb. Math., 205:10 (2014), 1387–1412
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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    Russian version PDF:202
    English version PDF:24
    References:62
    First page:37
     
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