On the structure of the Birkhoff-irregular set for some subshifts of finite type

Speaker: Sebastian Burgos (Penn State University)
Abstract: We study the set of irregular points for Birkhoff averages for a class of topologically mixing subshifts of finite type. It is well known that, despite the irregular set having zero measure for every invariant measure, it possesses full topological entropy and Hausdorff dimension. We establish that for these systems, the irregular set is not only abundant in its dimensional properties but also contains uncountably many pairwise disjoint subsets, each with full entropy and dimension.
Date: 19/11/2024 – 16:00
Room: https://meet.google.com/hhk-vvch-vdk