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Nelin. Dinam., 2014, Volume 10, Number 1, Pages 17–33 (Mi nd422)  

This article is cited in 5 scientific papers (total in 5 papers)

On topological classification of diffeomorphisms on 3-manifolds with two-dimensional surface attractors and repellers

Vyacheslav Z. Grines, Yulia A. Levchenko, Olga V. Pochinka

Nizhny Novgorod State University, Ul’yanova st. 10, Nizhny Novgorod, 603605, Russia

Abstract: We consider a class of diffeomorphisms on 3-manifolds which satisfy S. Smale's axiom $A$ such that their nonwandering set consists of two-dimensional surface basic sets. Interrelation between dynamics of such diffeomorphism and topology of the ambient manifold is studied. Also we establish that each considered diffeomorphism is $\Omega$-conjugated with a model diffeomorphism of mapping torus. Under certain assumptions on asymptotic properties of two-dimensional invariant manifolds of points from the basic sets, we obtain necessary and sufficient conditions of topological conjugacy of structurally stable diffeomorphisms from the considered class.

Keywords: diffeomorphism, basic set, topological conjugacy, attractor, repeller.

Full text: PDF file (431 kB)
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UDC: 517.938
MSC: 37E30
Received: 30.12.2013
Revised: 22.01.2014

Citation: Vyacheslav Z. Grines, Yulia A. Levchenko, Olga V. Pochinka, “On topological classification of diffeomorphisms on 3-manifolds with two-dimensional surface attractors and repellers”, Nelin. Dinam., 10:1 (2014), 17–33

Citation in format AMSBIB
\Bibitem{GriLevPoc14}
\by Vyacheslav~Z.~Grines, Yulia~A.~Levchenko, Olga~V.~Pochinka
\paper On topological classification of diffeomorphisms on 3-manifolds with two-dimensional surface attractors and repellers
\jour Nelin. Dinam.
\yr 2014
\vol 10
\issue 1
\pages 17--33
\mathnet{http://mi.mathnet.ru/nd422}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. Z. Grines, E. Ya. Gurevich, E. V. Zhuzhoma, S. Kh. Zinina, “Geteroklinicheskie krivye diffeomorfizmov Morsa–Smeila i separatory v magnitnom pole plazmy”, Nelineinaya dinam., 10:4 (2014), 427–438  mathnet
    2. Grines V.Z., Levchenko Yu.A., Medvedev V.S., Pochinka O.V., “On the Dynamical Coherence of Structurally Stable 3-Diffeomorphisms”, Regul. Chaotic Dyn., 19:4 (2014), 506–512  crossref  isi
    3. V. Z. Grines, Ye. V. Zhuzhoma, O. V. Pochinka, “Rough diffeomorphisms with basic sets of codimension one”, Journal of Mathematical Sciences, 225:2 (2017), 195–219  mathnet  crossref
    4. V. Z. Grines, T. V. Medvedev, O. V. Pochinka, “Dynamical Systems on 2-and 3-manifolds Introduction”, Dynamical Systems on 2- and 3-Manifolds, Developments in Mathematics, 46, Springer, 2016, XVII–XXVI  isi
    5. V. Z. Grines, O. V. Pochinka, A. A. Shilovskaya, “Diffeomorfizmy 3-mnogoobrazii s odnomernymi bazisnymi mnozhestvami prostorno raspolozhennymi na 2-torakh”, Zhurnal SVMO, 18:1 (2016), 17–26  mathnet  elib
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