Conjugacy of Morse-Smale diffeomorphisms with three nonwandering points
type: Item
instance of: scholarly article
title: Conjugacy of Morse-Smale diffeomorphisms with three nonwandering points
zbMATH Open document ID: 1412.37025
DOI: 10.1134/S0001434618110184
author: Vladislav S. Medvedev
author: Evgenii V. Zhuzhoma
published in: Mathematical Notes
publication date: 2019-03-19T00:00:00Z
review text: In [Math. Notes 92, No. 4, 497--512 (2012; Zbl 1280.37030); translation from Mat. Zametki 92, No. 4, 541--558 (2012); Dokl. Math. 84, No. 2, 604--606 (2011; Zbl 1279.37029); translation from Dokl. Akad. Nauk 440, No. 1, 11--14 (2011)] the authors described the topological structure of the underlying $n$-dimensional manifold $M^n$ of a Morse-Smale diffeomorphism $f: M^n\to M^n$ with a three-point nonwandering set. In [Sb. Math. 207, No. 5, 702--723 (2016; Zbl 1373.37086); translation from Mat. Sb. 207, No. 5, 69--92 (2016)] they presented necessary and sufficient conditions to obtain the topological equivalence of Morse-Smale flows with three equilibria. \par Now, in this paper, the authors obtain necessary and sufficient conjugacy conditions for Morse-Smale diffeomorphisms with a three-point nonwandering set. Their main theorem relates the conjugacy of two diffeomorphisms $f_1,f_2: M^n\to M^n$ with the local dynamical equivalent embedding of either the stable or the unstable sets of the saddles $s_1,s_2$ of $f_1,f_2$, respectively.
reviewed by: Matheus Cheque Bortolan
Mathematics Subject Classification ID: 37C15
Mathematics Subject Classification ID: 37D15
Mathematics Subject Classification ID: 37C05
Mathematics Subject Classification ID: 37D05
zbMATH DE Number: 7037793
zbMATH Keywords: Morse-Smale diffeomorphism
zbMATH Keywords: topological conjugacy
zbMATH Keywords: hyperbolic point
MaRDI profile type: Publication
cites work: On Topological Classification of Morse–Smale Diffeomorphisms
cites work: Q4888791
cites work: Differentiable dynamical systems
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full work available at URL: s0001434618110184
OpenAlex ID: W2907396379
Wikidata QID: Q128655781
description: scientific article; zbMATH DE number 7037793