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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2002, Volume 236, Pages 66–78
(Mi tm277)
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This article is cited in 10 scientific papers (total in 10 papers)
On Morse–Smale Diffeomorphisms without Heteroclinic Intersections on Three-Manifolds
Ch. Bonattia, V. Z. Grinesb, V. S. Medvedevc, E. Pekua a Université de Bourgogne
b Nizhnii Novgorod State Agricultural Academy
c Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod
Abstract:
A class of Morse–Smale diffeomorphisms is considered that do not admit heteroclinic intersections and are defined on three-manifolds. To each diffeomorphism f, we associate an enriched graph G(f) and, for each sink ω, we define a scheme S(ω) which is a link of tori, the Klein bottle, and simple closed curves embedded in S2×S1. We show that diffeomorphisms f1 and f2 are topologically conjugate if and only if (1) the corresponding graphs G(f1) and G(f2) are isomorphic and the permutations induced by the dynamics f1 and f2 on the vertices and edges of the graphs are conjugate; (2) two sinks corresponding to isomorphic vertices have equivalent schemes; and (3) for any two saddles corresponding to isomorphic vertices and having one-dimensional unstable manifolds, the corresponding pairs of curves in S2×S1 associated with the one-dimensional separatrices are concordantly embedded.
Received in December 2000
Citation:
Ch. Bonatti, V. Z. Grines, V. S. Medvedev, E. Peku, “On Morse–Smale Diffeomorphisms without Heteroclinic Intersections on Three-Manifolds”, Differential equations and dynamical systems, Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko, Trudy Mat. Inst. Steklova, 236, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 66–78; Proc. Steklov Inst. Math., 236 (2002), 58–69
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https://www.mathnet.ru/eng/tm277 https://www.mathnet.ru/eng/tm/v236/p66
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