Explosion of smoothness from a point to everywhere for conjugacies between Markov families

• Tipo: Artigo em Revista Científica Internacional
• Data: 2001

Autores

F. Ferreira (Autor) Outra; A. A. Pinto (Autor) FCUP

Revista

Título: Dynamical Systems

Vol. 16 Nº 2

Páginas: 193-212

ISSN: 1468-9367

Editora: Taylor & Francis

Indexação

ISI Web of Knowledge - 9 Citações

Scopus - 9 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: P-000-VA1

DOI: 10.1080/02681110110038756

Resumo (PT): For uniformly asymptotically affine (uaa) Markov maps on train tracks, we prove the following type of rigidity result: if a topological conjugacy between them is (uaa) at a point in the train track then the conjugacy is (uaa) everywhere. In particular, our methods apply to the case in which the domains of the Markov maps are Cantor sets. We also present similar statements for (uaa) and C^r Markov families. These results generalize the similar ones of Sullivan and de Faria for C^r expanding circle maps with r > 1 and have useful applications to hyperbolic dynamics on surfaces and laminations.

Abstract (EN): For uniformly asymptotically affine (uaa) Markov maps on train tracks, we prove the following type of rigidity result: if a topological conjugacy between them is (uaa) at a point in the train track then the conjugacy is (uaa) everywhere. In particular, our methods apply to the case in which the domains of the Markov maps are Canter sets. We also present similar statements for (uaa:) and C-r Markov families. These results generalize the similar ones of Sullivan and de Faria for C-r expanding circle maps with r > 1 and have useful applications to hyperbolic dynamics on surfaces and laminations.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 20