Transfer operators and dimension of bad sets for non-uniform fuchsian lattices

Abstract: The set of badly approximable real numbers admits an exhaustion in sets Bad(c) with c>0, whose dimension goes to zero as c goes to zero. D. Hensley computed the asymptotic for the dimension up to the first order in c, via an estimate for the dimension of the set of real numbers whose continued fraction has partial quotiens bounded by a fixed parameter. We consider diophantine approximations by parabolic fiwed points of any non-uniform lattice in PSL(2,R) and the corresponding notion of badly approximable real numbers. We compute the dimension of the set of such points up to the first order in c>0, via the thermodynamic method of Ruelle and Bowen. Geometric good approximations are related to a notion of bounded partial quotients for the Bowen-Series expansion. This gives a family of Cantor sets and associated quasi-compact transfer operators, with simple and positive maximal eigenvalue. Then perturbative analysis of spectra applies.

dynamical systems

Audience: researchers in the topic

Bremen Online Dynamics Seminar

Series comments: Talks are approx. 55 min plus discussion. Talks are not recorded.

The meeting links are announced via the seminar mailing list, a few days before the talks. To subscribe please send an email with subject "subscribe" (without the ") to bods-request@mailman.zfn.uni-bremen.de or visit the webpage

mailman.zfn.uni-bremen.de/cgi-bin/mailman/listinfo/bods

This mailing list is used only for the purpose of the announcements. No spam! You can unsubscribe at any time following the instructions in the emails or on the webpage above.