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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 310, Pages 119–134
DOI: https://doi.org/10.4213/tm4096 (Mi tm4096) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On Realization of Topological Conjugacy Classes of Morse–Smale Cascades on the Sphere $S^n$

V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev

National Research University Higher School of Economics, Bol'shaya Pecherskaya ul. 25/12, Nizhny Novgorod, 603155 Russia
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DOI: https://doi.org/10.4213/tm4096
Abstract: We consider the class $G(S^n)$ of orientation-preserving Morse–Smale diffeomorphisms defined on the sphere $S^n$ of dimension $n\geq 4$ under the assumption that the invariant manifolds of different saddle periodic points are disjoint. For diffeomorphisms in this class, we describe an algorithm for constructing representatives of all topological conjugacy classes.
Funding agency Grant number
Russian Science Foundation 17-11-01041
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1931
This work is supported by the Russian Science Foundation under grant 17-11-01041, except for the proof of Lemma 1. The work on the proof of Lemma 1 is supported by the HSE Laboratory of Dynamical Systems and Applications and the Ministry of Science and Higher Education of the Russian Federation under grant 075-15-2019-1931.
Received: December 2, 2019
Revised: December 2, 2019
Accepted: April 6, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 310, Pages 108–123
DOI: https://doi.org/10.1134/S0081543820050089
Bibliographic databases:
Document Type: Article
UDC: 517.938
Language: Russian
Citation: V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, “On Realization of Topological Conjugacy Classes of Morse–Smale Cascades on the Sphere $S^n$”, Selected issues of mathematics and mechanics, Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov, Trudy Mat. Inst. Steklova, 310, Steklov Math. Inst., Moscow, 2020, 119–134; Proc. Steklov Inst. Math., 310 (2020), 108–123
Citation in format AMSBIB
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\paper On Realization of Topological Conjugacy Classes of Morse--Smale Cascades on the Sphere $S^n$
\inbook Selected issues of mathematics and mechanics
\bookinfo Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov
\serial Trudy Mat. Inst. Steklova
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\vol 310
\pages 119--134
\publ Steklov Math. Inst.
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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