Arc exchange systems and renormalization

• Type: Article in International Scientific Journal
• Date: 2010

Authors

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

Journal

Title: Journal of Difference Equations and Applications

Vol. 16 No. 12

Pages: 347-371

ISSN: 1023-6198

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 3 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 25