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Tr. Mat. Inst. Steklova, 2002, Volume 236, Pages 212–217 (Mi tm291)  

This article is cited in 2 scientific papers (total in 2 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).

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English version:
Proceedings of the Steklov Institute of Mathematics, 2002, 236, 201–205

Bibliographic databases:
UDC: 517.917+513.83
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, Tr. Mat. Inst. Steklova, 236, Nauka, MAIK Nauka/Inteperiodika, M., 2002, 212–217; Proc. Steklov Inst. Math., 236 (2002), 201–205

Citation in format AMSBIB
\Bibitem{KruTal02}
\by E.~V.~Kruglov, E.~A.~Talanova
\paper On the Realization of Morse--Smale Diffeomorphisms with Heteroclinic Curves on a 3-Sphere
\inbook Differential equations and dynamical systems
\bookinfo Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko
\serial Tr. Mat. Inst. Steklova
\yr 2002
\vol 236
\pages 212--217
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm291}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1931021}
\zmath{https://zbmath.org/?q=an:1013.37024}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2002
\vol 236
\pages 201--205


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    This publication is cited in the following articles:
    1. V. Z. Grines, E. V. Zhuzhoma, V. S. Medvedev, O. V. Pochinka, “Global attractor and repeller of Morse–Smale diffeomorphisms”, Proc. Steklov Inst. Math., 271 (2010), 103–124  mathnet  crossref  mathscinet  isi  elib
    2. O. V. Pochinka, E. V. Kruglov, A. Yu. Dolgonosova, “Stsenarii peresoedineniya v korone Solntsa s prostoi diskretizatsiei”, Nelineinaya dinam., 13:4 (2017), 573–578  mathnet  crossref  elib
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