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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2002, Volume 236, Pages 212–217
(Mi tm291)
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This article is cited in 3 scientific papers (total in 3 papers)
On the Realization of Morse–Smale Diffeomorphisms with Heteroclinic Curves on a 3-Sphere
E. V. Kruglov, E. A. Talanova Nizhnii Novgorod State Agricultural Academy
Abstract:
A Morse–Smale diffeomorphism is constructed on a three-dimensional sphere whose nonwandering set consists of one sink, one source, and two saddle fixed points. The two-dimensional manifolds of the saddle fixed points intersect along a unique one-dimensional heteroclinic curve. This example is constructed so that the one-dimensional separatrices of the saddle fixed points may represent wildly embedded arcs, which results in the realization of at least two topologically nonconjugate diffeomorphisms of the type under consideration. The example constructed shows an essential difference between the behavior of discrete dynamical systems on three-dimensional manifolds and analogous systems with continuous time (flows).
Received in December 2000
Citation:
E. V. Kruglov, E. A. Talanova, “On the Realization of Morse–Smale Diffeomorphisms with Heteroclinic Curves on a 3-Sphere”, 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, 212–217; Proc. Steklov Inst. Math., 236 (2002), 201–205
Linking options:
https://www.mathnet.ru/eng/tm291 https://www.mathnet.ru/eng/tm/v236/p212
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Abstract page: | 305 | Full-text PDF : | 82 | References: | 34 |
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