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Matematicheskie Zametki, 2003, Volume 74, Issue 3, Pages 369–386
DOI: https://doi.org/10.4213/mzm271 (Mi mzm271) 		 
This article is cited in 25 scientific papers (total in 25 papers)

On Morse–Smale Diffeomorphisms with Four Periodic Points on Closed Orientable Manifolds

V. Z. Grinesa, E. V. Zhuzhomab, V. S. Medvedevc

a Nizhnii Novgorod State Agricultural Academy
b Nizhny Novgorod State Technical University
c Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod
Full-text PDF (334 kB) Citations (25)
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DOI: https://doi.org/10.4213/mzm271
Abstract: We study Morse–Smale diffeomorphisms of n-manifolds with four periodic points which are the only periodic points. We prove that for $n= 3$ these diffeomorphisms are gradient-like and define a class of diffeomorphisms inevitably possessing a nonclosed heteroclinic curve. For $n\ge4$, we construct a complete conjugacy invariant in the class of diffeomorphisms with a single saddle of codimension one.
Received: 12.09.2001
Revised: 22.05.2002
English version:
Mathematical Notes, 2003, Volume 74, Issue 3, Pages 352–366
DOI: https://doi.org/10.1023/A:1026154718469
Bibliographic databases:
UDC: 517.9+513.83
Language: Russian
Citation: V. Z. Grines, E. V. Zhuzhoma, V. S. Medvedev, “On Morse–Smale Diffeomorphisms with Four Periodic Points on Closed Orientable Manifolds”, Mat. Zametki, 74:3 (2003), 369–386; Math. Notes, 74:3 (2003), 352–366
Citation in format AMSBIB
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    • This publication is cited in the following 25 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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