Agnieszka Zelerowicz - Highly irregular orbits for subshifts of finite type

In their recent paper, S. Kiriki, Y. Nakano, and T. Soma introduced a concept of pointwise emergence to measure the complexity of irregular orbits. They constructed a residual subset of the full shift with high pointwise emergence. In our joint work with Yushi Nakano we consider the set of points with high pointwise emergence for topologically mixing subshifts of finite type. We show that this set has full topological entropy, full Hausdorff dimension, and full topological pressure for any Hölder continuous potential. Furthermore, we show that this set belongs to a certain class of sets with large intersection property.

Agnieszka Zelerowicz is currently a postdoc at the University of Maryland, College Park