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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  
Dates: 


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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