Pinto, A. A. and Rand, D. A. (David A.). (2002) Teichmüller spaces and HR structures for hyperbolic surface dynamics. Ergodic Theory and Dynamical Systems, Vol.22 (No.6). pp. 1905-1931. ISSN 0143-3857

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Abstract

We construct a Teichmüller space for the C^{1+}-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 C^{1+}-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 C^{1+}-conjugacy class. Finally, we introduce solenoid functions and show that they provide a good Teichmüller space.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Teichmüller spaces, Hyperbolic spaces, Surfaces, Algebraic, Anosov diffeomorphisms, Topological dynamics
Journal or Publication Title:	Ergodic Theory and Dynamical Systems
Publisher:	Cambridge University Press
ISSN:	0143-3857
Date:	December 2002
Volume:	Vol.22
Number:	No.6
Page Range:	pp. 1905-1931
Identification Number:	10.1017/S0143385702000792
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/790

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