Multifractal analysis of Birkhoff averages for non-uniformly expanding Markov interval maps

2020/12/04 金 14:00 - 17:00
Johannes Jaerisch
名古屋大学 (Nagoya University)

For non-uniformly expanding Markov interval maps we establish a conditional variational formula for the mixed multifractal spectrum of Birkhoff averages of countably many observables, in terms of the Hausdorff dimension of invariant probability measures. By applying this result to the Renyi map, we are able to investigate the arithmetic mean and the asymptotic frequency of digits of the backward continued fraction expansion of real numbers. We also discuss applications to the Bowen-Series map associated with Fuchsian groups with parabolic elements, which allows us to study cusp windings of the geodesic flow on the associated hyperbolic surface. This is a joint work with Hiroki Takahasi (Keio University).