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  • Cited by 4
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Almeida, João P. and Pinto, Alberto A. 2016. Anosov Diffeomorphisms and $${\gamma}$$ γ -Tilings. Communications in Mathematical Physics, Vol. 345, Issue. 2, p. 435.

    Pinto, A.A. and Rand, D.A. 2010. Train tracks withC1+self-renormalizable structures. Journal of Difference Equations and Applications, Vol. 16, Issue. 8, p. 945.

    Pinto, A.A. Rand, D.A. and Ferreira, F. 2007. Cantor exchange systems and renormalization. Journal of Differential Equations, Vol. 243, Issue. 2, p. 593.

    Pinto, A.A. Rand, D.A. and Ferreira, F. 2007. Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics. Journal of Differential Equations, Vol. 243, Issue. 2, p. 168.

  • Ergodic Theory and Dynamical Systems, Volume 22, Issue 6
  • December 2002, pp. 1905-1931

Teichmüller spaces and HR structures for hyperbolic surface dynamics

  • A. A. PINTO (a1) and D. A. RAND (a2)
  • DOI:
  • Published online: 21 November 2002

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.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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