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Regular and Chaotic Dynamics, 2014, Volume 19, Issue 4, Pages 506–512
DOI: https://doi.org/10.1134/S1560354714040066 (Mi rcd177) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On the Dynamical Coherence of Structurally Stable 3-diffeomorphisms

Vyacheslav Z. Grines, Yulia A. Levchenko, Vladislav S. Medvedev, Olga V. Pochinka

Nizhny Novgorod State University, pr. Gagarina 23, Nizhny Novgorod, 603950 Russia
Citations (6)
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DOI: https://doi.org/10.1134/S1560354714040066
Abstract: We prove that each structurally stable diffeomorphism ff on a closed 3-manifold M3M3 with a two-dimensional surface nonwandering set is topologically conjugated to some model dynamically coherent diffeomorphism.
Keywords: structural stability, surface basic set, partial hyperbolicity, dynamical coherence.
Funding agency Grant number
Russian Foundation for Basic Research 12-01- 00672-a
13-01-12452-ofi-m
This work was supported by the Russian Foundation for Basic Research (project nos. 12-01-00672-a, 13-01-12452-ofi-m).
Received: 20.03.2014
Accepted: 05.05.2014
Bibliographic databases:
Document Type: Article
MSC: 37D20, 37D30
Language: English
Citation: Vyacheslav Z. Grines, Yulia A. Levchenko, Vladislav S. Medvedev, Olga V. Pochinka, “On the Dynamical Coherence of Structurally Stable 3-diffeomorphisms”, Regul. Chaotic Dyn., 19:4 (2014), 506–512
Citation in format AMSBIB
\Bibitem{GriLevMed14}
\by Vyacheslav~Z.~Grines, Yulia~A.~Levchenko, Vladislav~S.~Medvedev, Olga~V.~Pochinka
\paper On the Dynamical Coherence of Structurally Stable 3-diffeomorphisms
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 4
\pages 506--512
\mathnet{http://mi.mathnet.ru/rcd177}
\crossref{https://doi.org/10.1134/S1560354714040066}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3240983}
\zmath{https://zbmath.org/?q=an:1335.37010}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000340380900006}
Linking options:
  • https://www.mathnet.ru/eng/rcd177
  • https://www.mathnet.ru/eng/rcd/v19/i4/p506
    • This publication is cited in the following 6 articles:
    1. Vyacheslav Z. Grines, Olga V. Pochinka, Ekaterina E. Chilina, “On Homeomorphisms of Three-Dimensional Manifolds with Pseudo-Anosov Attractors and Repellers”, Regul. Chaotic Dyn., 29:1 (2024), 156–173  mathnet  crossref
    2. V. Z. Grines, O. V. Pochinka, E. E. Chilina, “Dynamics of 3-Homeomorphisms with Two-Dimensional Attractors and Repellers”, J Math Sci, 270:5 (2023), 683  crossref
    3. Vyacheslav Z. Grines, Elena Ya. Gurevich, Olga V. Pochinka, “On the Number of Heteroclinic Curves of Diffeomorphisms with Surface Dynamics”, Regul. Chaotic Dyn., 22:2 (2017), 122–135  mathnet  crossref
    4. V. Z. Grines, T. V. Medvedev, O. V. Pochinka, “Introduction to Dynamical Systems”, Dynamical Systems on 2- and 3-Manifolds, Developments in Mathematics, 46, Springler, 2016, 1–26  crossref  mathscinet  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
    6. 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
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