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Mat. Sb., 2014, Volume 205, Number 10, Pages 19–46 (Mi msb8328)  

This article is cited in 4 scientific papers (total in 4 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

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

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8328

Full text: PDF file (934 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:10, 1387–1412

Bibliographic databases:

UDC: 517.938
MSC: Primary 37D15; Secondary 37C05, 37C15, 37E30
Received: 15.01.2014

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Vyacheslav Z. Grines, Dmitry S. Malyshev, Olga V. Pochinka, Svetlana Kh. Zinina, “Efficient Algorithms for the Recognition of Topologically Conjugate Gradient-like Diffeomorhisms”, Regul. Chaotic Dyn., 21:2 (2016), 189–203  mathnet  crossref  mathscinet
    2. V. Z. Grines, E. V. Zhuzhoma, O. V. Pochinka, “Sistemy Morsa–Smeila i topologicheskaya struktura nesuschikh mnogoobrazii”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 61, RUDN, M., 2016, 5–40  mathnet
    3. V. E. Kruglov, D. S. Malyshev, O. V. Pochinka, “A multicolour graph as a complete topological invariant for $\Omega$-stable flows without periodic trajectories on surfaces”, Sb. Math., 209:1 (2018), 96–121  mathnet  crossref  crossref  adsnasa  isi  elib
    4. 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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