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Regular and Chaotic Dynamics, 2006, Volume 11, Issue 2, Pages 225–246
DOI: https://doi.org/10.1070/RD2006v011n02ABEH000347
(Mi rcd670)
 

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

On the 70th birthday of L.P. Shilnikov

Expanding attractors

V. Z. Grinesa, E. V. Zhuzhomab

a Department of Mathematics, Agriculture Academy of Nizhny Novgorod, 97 Gagarin str., 603107 Nizhny Novgorod, Russia
b Department of Applied Mathematics, Nizhny Novgorod State Technical University, 24 Minin str., 603600 Nizhny Novgorod, Russia
Citations (5)
Abstract: The article is a survey on local and global structures (including classification results) of expanding attractors of diffeomorphisms $f : M \to M$ of a closed smooth manifold $M$. Beginning with the most familiar expanding attractors (Smale solenoid; DA-attractor; Plykin attractor; Robinson–Williams attractors), one reviews the Williams theory, Bothe's classification of one-dimensional solenoids in 3-manifolds, Grines–Plykin–Zhirov's classification of one-dimensional expanding attractors on surfaces, and Grines–Zhuzhoma's classification of codimension one expanding attractors of structurally stable diffeomorphisms. The main theorems are endowed with ideas of proof.
Keywords: Axiom A diffeomorphisms, (codimension one) expanding attractors, structurally stable diffeomorphisms, hyperbolic automorphisms.
Received: 28.05.2005
Accepted: 15.11.2005
Bibliographic databases:
Document Type: Article
MSC: 37D20, 37C70, 37C15
Language: English
Citation: V. Z. Grines, E. V. Zhuzhoma, “Expanding attractors”, Regul. Chaotic Dyn., 11:2 (2006), 225–246
Citation in format AMSBIB
\Bibitem{GriZhu06}
\by V. Z. Grines, E. V. Zhuzhoma
\paper Expanding attractors
\jour Regul. Chaotic Dyn.
\yr 2006
\vol 11
\issue 2
\pages 225--246
\mathnet{http://mi.mathnet.ru/rcd670}
\crossref{https://doi.org/10.1070/RD2006v011n02ABEH000347}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2245079}
\zmath{https://zbmath.org/?q=an:1164.37317}
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  • This publication is cited in the following 5 articles:
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