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Teichmüller spaces and HR structures for hyperbolic surface dynamics
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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. 19051931. ISSN 01433857

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Official URL: http://dx.doi.org/10.1017/S0143385702000792
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 onetoone 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:  01433857 
Official Date:  December 2002 
Volume:  Vol.22 
Number:  No.6 
Page Range:  pp. 19051931 
Identification Number:  10.1017/S0143385702000792 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Open Access 
References:  [1] R. Abraham and J. Robbin. Transversal Mappings and Flows. W. A. Benjamin, New York, 1967. 
URI:  http://wrap.warwick.ac.uk/id/eprint/790 
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