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
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.
diffeomorphism, basic set, topological conjugacy, attractor, repeller.
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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
\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.
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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
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
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
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
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
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