Expanding attractors

    2006, Volume 11, Number 2, pp.  225-246

    Author(s): Grines V. Z., Zhuzhoma E. V.

    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
    Citation: Grines V. Z., Zhuzhoma E. V., Expanding attractors , Regular and Chaotic Dynamics, 2006, Volume 11, Number 2, pp. 225-246


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