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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
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
Citation:
V. Z. Grines, E. V. Zhuzhoma, “Expanding attractors”, Regul. Chaotic Dyn., 11:2 (2006), 225–246
Linking options:
https://www.mathnet.ru/eng/rcd670 https://www.mathnet.ru/eng/rcd/v11/i2/p225
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