### Dirichlet Systems, singular points and extremal sets

Ergodic Theory and Dynamical Systems Seminar

12th December 2019, 3:15 pm – 4:15 pm

Fry Building, 2.04 - 2nd Floor Seminar Room

Beresnevich, Ghosh, Simmons and Velani introduced the notion of singular points and extremal sets associated with the limit sets of Kleinian groups. Inspired by ideas in their paper and the fundamental notion of ubiquity, we introduce a general framework called Dirichlet systems and extend the notion of singularity and extremality to this set-up. Within this set-up we are able to recover the classical 1-dimensional theory and some of the results obtained by Beresnevich, et al, and further show that Dirichlet systems imply a version of ubiquity. In this talk I will give details of this framework and discuss the associated notions of singularity and extremality within it.

This is joint work with Sky Brewer.

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