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Mat. Zametki, 2013, Volume 94, Issue 1, Pages 109–121 (Mi mz9682)  

How Many Different Cascades on a Surface Can Have Coinciding Hyperbolic Attractors?

A. Yu. Zhirov

Moscow State Aviation Technological University, Moscow

Abstract: It is shown that the number of essentially nonconjugate (i.e., not being iterations of topologically conjugate) diffeomorphisms of a surface having homeomorphic one-dimensional hyperbolic attractors can be arbitrarily large, provided that the genus of the surface is large enough. A lower bound for this number depending on the surface genus is given. The corresponding result for pseudo-Anosov homeomorphisms is stated.

Keywords: surface diffeomorphism, cascade, essentially nonconjugate surface diffeomorphisms, one-dimensional hyperbolic attractor, pseudo-Anosov homeomorphism.

DOI: https://doi.org/10.4213/mzm9682

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English version:
Mathematical Notes, 2013, 94:1, 96–106

Bibliographic databases:

Document Type: Article
UDC: 517.938.5
Received: 02.05.2012
Revised: 25.10.2012

Citation: A. Yu. Zhirov, “How Many Different Cascades on a Surface Can Have Coinciding Hyperbolic Attractors?”, Mat. Zametki, 94:1 (2013), 109–121; Math. Notes, 94:1 (2013), 96–106

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