Topic: Ruelle Property: Old and New
Speaker: Professor Michel Zinsmeister
Event date: 6/28/2019
Event time: 16:30 pm
Venue: Lecture Hall 1506, Building 9
Sponsor: School of Mathematics and Statistics, Institute of Science and Technology
Abstract: Let S be aRiemann surface and T(S) its Teichmuller space. One can naturally attach toeach element of T(S) a quasi-Fuchsian group whose limit set may be fractal.Ruelle has proven that the Hausdorff dimension of this limit set is areal-analytic function on T(S) when S is compact: we say that compact Riemannsurfaces have Ruelle property. What are the surfaces sharing this property? Inthis talk I will survey what is known about this problem, in particular I willshow that there exists an infinitely generated Fuchsian group whose corresponding surface has Ruelle’s property.