RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Nelin. Dinam.: Year: Volume: Issue: Page: Find

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

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)
References: PDF file   HTML file
UDC: 517.938
MSC: 37E30
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} 

• http://mi.mathnet.ru/eng/nd422
• http://mi.mathnet.ru/eng/nd/v10/i1/p17

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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
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
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
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
•  Number of views: This page: 260 Full text: 74 References: 47