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Matematicheskie Zametki, 2013, Volume 94, Issue 1, Pages 109–121
DOI: https://doi.org/10.4213/mzm9682 (Mi mzm9682) 		 
How Many Different Cascades on a Surface Can Have Coinciding Hyperbolic Attractors?

A. Yu. Zhirov

Moscow State Aviation Technological University, Moscow
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DOI: https://doi.org/10.4213/mzm9682
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.
Received: 02.05.2012
Revised: 25.10.2012
English version:
Mathematical Notes, 2013, Volume 94, Issue 1, Pages 96–106
DOI: https://doi.org/10.1134/S0001434613070092
Bibliographic databases:
Document Type: Article
UDC: 517.938.5
Language: Russian
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
Citation in format AMSBIB
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