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

• Type: Article in International Scientific Journal
• Date: 2001

Authors

Ferreira, F (Author) Other; Alberto A. Pinto (Author) FCUP

Journal

Title: Dynamical Systems

Vol. 16 No. 2

Pages: 193-212

ISSN: 1468-9367

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 9 Citations

Scopus - 9 Citations

Other information

Authenticus ID: P-000-VA1

DOI: 10.1080/02681110110038756

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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 20