English

On Ruelle's property

Complex Variables 2019-06-05 v1

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-Zinsmeister's results by proving that all convergence Fuchsian groups of the first kind fail to have Ruelle's property. At last, we also give some results about the second kind Fuchsian groups.

Cite

@article{arxiv.1906.01291,
  title  = {On Ruelle's property},
  author = {Huo Shengjin and Michel Zinsmeister},
  journal= {arXiv preprint arXiv:1906.01291},
  year   = {2019}
}

Comments

11 pages

R2 v1 2026-06-23T09:40:43.967Z