Teichmuller spaces and HR structures for hyperbolic surface dynamics

• Type: Article in International Scientific Journal
• Date: 2002

Authors

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

Journal

Title: Ergodic Theory and Dynamical Systems

Vol. 22

Pages: 1905-1931

ISSN: 0143-3857

Publisher: Cambridge University Press

Indexing

ISI Web of Knowledge - 11 Citations

Scopus - 13 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-M63

DOI: 10.1017/s0143385702000792

Abstract (EN): We construct a Teichmuller space for the C1+-conjugacy classes of hyperbolic dynamical systems on surfaces. After introducing the notion of an HR structure which associates an affine structure with each of the stable and unstable laminations, we show that there is a one-to-one correspondence between these HR structures and the C1+-conjugacy classes. As part of the proof we construct a canonical representative dynamical system for each HR structure. This has the smoothest holonomies of any representative of the corresponding C1+-conjugacy class. Finally, we introduce solenoid functions and show that they provide a good Teichmuller space.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 27