Arc exchange systems and renormalization

• Tipo: Artigo em Revista Científica Internacional
• Data: 2010

Autores

Pinto, AA (Autor) FCUP; Rand, DA (Autor) Outra; Ferreira, F (Autor) Outra

Revista

Título: Journal of Difference Equations and Applications

Vol. 16 Nº 12

Páginas: 347-371

ISSN: 1023-6198

Editora: Taylor & Francis

Indexação

ISI Web of Knowledge - 1 Citação

Scopus - 3 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: P-003-BKD

DOI: 10.1080/10236190802422059

Abstract (EN): We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 25