[BODS] Luca Marchese, Jul 28th, 3:30 pm CEST

[Anke POHL]

Dear all,

For the next talk in the Bremen Online Dynamics Seminar (BODS) we
welcome:

Speaker: Luca Marchese (U Bologna)
Date and time: Monday, Jul 18th, 2022, 3:30-4:30 pm CEST
(+ ca. 15 min Q&A)

Link: 
https://uni-bremen.zoom.us/j/4528023413?pwd=ZUFqR0xXM0JMNU1hcnlQQnNmMlhEQT09

For full link information see below.

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Title:
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 fixed 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.
****

For the growing list of future talks please refer to
researchseminars.org/seminar/BODS

Looking forward to seeing many of you there,
Anke

****

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-- 
Prof. Dr. Anke Pohl
University of Bremen
Department 3 - Mathematics
Institute for Dynamical Systems
Bibliothekstr. 5
28359 Bremen
Germany

http://user.math.uni-bremen.de/apohl/

Telefone: +49-421-218-63661
Email: apohl at uni-bremen.de
Office: MZH 4150