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ruelle’s property

Ergodic Theory and Dynamical Systems (1)

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1 results

On Ruelle’s property
Part of
- Riemann surfaces
SHENGJIN HUO, MICHEL ZINSMEISTER
Journal:

Ergodic Theory and Dynamical Systems / Volume 42 / Issue 4 / April 2022

Published online by Cambridge University Press:

02 February 2021, pp. 1474-1486

Print publication:

April 2022
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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]