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On Ruelle’s property

Part of: Riemann surfaces

Published online by Cambridge University Press:  02 February 2021

SHENGJIN HUO Open the ORCID record for SHENGJIN HUO [Opens in a new window]  and
MICHEL ZINSMEISTER
SHENGJIN HUO*
Affiliation:
Department of Mathematics, Tiangong University, Tianjin300387, China
MICHEL ZINSMEISTER
Affiliation:
Institut Denis Poisson, COST, Université d’Orléans BP 6749, 45067 Orléans Cedex 2, France (e-mail: zins@unvi-orleans.fr)
*
e-mail: huoshengjin@tiangong.edu.cn
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Abstract

In this paper we investigate the range of validity of Ruelle’s property. First, we show that every finitely generated Fuchsian group has Ruelle’s property. We also prove the existence of an infinitely generated Fuchsian group satisfying Ruelle’s property. Concerning the negative results, we first generalize Astala and Zinsmeister’s results [Mostow rigidity and Fuchsian groups. C. R. Math. Acad. Sci. Paris311 (1990), 301–306; Teichmüller spaces and BMOA. Math. Ann.289 (1991), 613–625] by proving that all convergence-type Fuchsian groups of the first kind fail to have Ruelle’s property. Finally, we give some results about second-kind Fuchsian groups. [-3.2pc]

Keywords

iterated function systemMarkov mapRuelle’s property

MSC classification

Primary: 30F35: Fuchsian groups and automorphic functions
Secondary: 30F60: Teichmüller theory
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 4 , April 2022 , pp. 1474 - 1486
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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