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Teichmüller spaces and HR structures for hyperbolic surface dynamics

Published online by Cambridge University Press:  21 November 2002

A. A. PINTO  and
D. A. RAND
A. A. PINTO
Affiliation:
DMA, Faculdade de Ciências, Universidade do Porto, 4000 Porto, Portugal (e-mail: [email protected])
D. A. RAND
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK (e-mail: [email protected])
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 6 , December 2002 , pp. 1905 - 1931
Copyright
2002 Cambridge University Press

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