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SUMMARY:Luca Marchese ((University of Bologna))
DTSTART:20220718T133000Z
DTEND:20220718T144500Z
DTSTAMP:20260423T021432Z
UID:BODS/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BODS/30/">Tr
 ansfer operators and dimension of bad sets for non-uniform fuchsian lattic
 es</a>\nby Luca Marchese ((University of Bologna)) as part of Bremen Onlin
 e Dynamics Seminar\n\n\nAbstract\nThe set of badly approximable real numbe
 rs 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 dimensi
 on up to the first order in c\, via an estimate for the dimension of the s
 et of real numbers whose continued fraction has partial quotiens bounded b
 y a fixed parameter. We consider diophantine approximations by parabolic f
 iwed 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 m
 ethod of Ruelle and Bowen. Geometric good approximations are related to a 
 notion of bounded partial quotients for the Bowen-Series expansion. This g
 ives a family of Cantor sets and associated quasi-compact transfer operato
 rs\, with simple and positive maximal eigenvalue. Then perturbative analys
 is of spectra applies.\n
LOCATION:https://researchseminars.org/talk/BODS/30/
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