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.
Idioma:
Inglês
Tipo (Avaliação Docente):
Científica
Nº de páginas:
24