Please use this identifier to cite or link to this item: http://hdl.handle.net/10216/93226
Author(s): Pinto, AA
Rand, DA
Feffeira, F
Title: Cantor exchange systems and renormalization
Issue Date: 2007
Abstract: We prove a one-to-one correspondence between (i) C1+ conjugacy classes of C1+H Cantor exchange systems that are C1+H fixed points of renormalization and (ii) C1+ conjugacy classes of C1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. However, we prove that there is no C1+alpha Cantor exchange system, with bounded geometry, that is a C1+alpha fixed point of renormalization with regularity alpha greater than the Hausdorff dimension of its invariant Cantor set. (C) 2007 Published by Elsevier Inc.
Description: We prove a one-to-one correspondence between (i) C1+ conjugacy classes of C^{1+H} Cantor exchangesystems that are C^{1+H} fixed points of renormalization and (ii) C^{1+} conjugacy classes of C^{1+H} diffeomorphismsf with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutelycontinuous with respect to the Hausdorff measure on Λ. However, we prove that there is no C^{1+α} Cantorexchange system, with bounded geometry, that is a C^{1+α} fixed point of renormalization with regularity αgreater than the Hausdorff dimension of its invariant Cantor set.
Subject: Matemática
Mathematics
URI: http://hdl.handle.net/10216/93226
Document Type: Artigo em Revista Científica Internacional
Rights: restrictedAccess
Appears in Collections:FCUP - Artigo em Revista Científica Internacional

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