Cantor exchange systems and renormalization

• Type: Article in International Scientific Journal
• Date: 2007

Authors

Pinto, AA (Author) FCUP; Rand, DA (Author) Other; Feffeira, F (Author) Other

Journal

Title: Journal of Differential Equations

Vol. 243

Pages: 593-616

ISSN: 0022-0396

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 6 Citations

Scopus - 7 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-004-5RP

DOI: 10.1016/j.jde.2007.09.014

Resumo (PT): 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.

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 24