Modul:   MAT760  Ergodic theory and dynamical systems seminar

Hausdorff dimension of exact sets in Ahlfors regular spaces

Vortrag von Dr. Prasuna Bandi

Sprecher eingeladen von: Prof. Dr. Alexander Gorodnik

Datum: 08.05.23  Zeit: 13.30 - 14.30  Raum: ETH HG G 43

In Diophantine approximation, it is a classical problem to determine the size of the sets related to \(\psi\) approximable set for a given non-increasing function \(\psi\). Bugeaud determined the Hausdorff dimension of the exact \(\psi\) approximable set answering a question posed by Beresnevich, Dickinson, and Velani. We compute the Hausdorff dimension of the exact set in the general setup of Ahlfors regular spaces. Our result applies to approximation by orbits of fixed points of a wide class of discrete groups of isometries acting on the boundary of hyperbolic metric spaces. This is joint work with Anish Ghosh and Debanjan Nandi.