Geodesic
How Many Different Cascades on a Surface Can Have Coinciding Hyperbolic Attractors?
Matematičeskie zametki, Tome 94 (2013) no. 1, pp. 109-121.

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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, essentially nonconjugate surface diffeomorphisms, one-dimensional hyperbolic attractor, pseudo-Anosov homeomorphism.
Mots-clés : cascade 
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A. Yu. Zhirov. How Many Different Cascades on a Surface Can Have Coinciding Hyperbolic Attractors?. Matematičeskie zametki, Tome 94 (2013) no. 1, pp. 109-121. http://geodesic.mathdoc.fr/item/MZM_2013_94_1_a8/

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