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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. 1905-1931. doi:10.1017/S0143385702000792 ISSN 0143-3857.
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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 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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
Official Date: | December 2002 | ||||
Dates: |
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Volume: | Vol.22 | ||||
Number: | No.6 | ||||
Page Range: | pp. 1905-1931 | ||||
DOI: | 10.1017/S0143385702000792 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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