Please use this identifier to cite or link to this item:
https://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 exchange systems that are C^{1+H} fixed points of renormalization and (ii) C^{1+} conjugacy classes of C^{1+H} diffeomorphisms f with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Λ. However, we prove that there is no C^{1+α} Cantor exchange system, with bounded geometry, that is a C^{1+α} fixed point of renormalization with regularity α greater than the Hausdorff dimension of its invariant Cantor set. |
Subject: | Matemática Mathematics |
Scientific areas: | Ciências exactas e naturais::Matemática Natural sciences::Mathematics |
URI: | https://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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