Consider a nested family of targets shrinking at a specified rate and a given flow, we want to understand the set of points that hit these targets infinitely often under the flow. One way to examine this set is to determine under what conditions this set has full measure. This question is closely related to the Borel Cantilli lemma and also gives rise to logarithm laws. In joint work with Spencer Dowdall we examine this particular question for Teichmuller flow on the moduli space of unit-area quadratic differentials.
The Shrinking Target Problem in the Context of Moduli Spaces of Translation Surfaces
Grace Work, University of Wisconsin-MadisonAuthors: Spencer Dowdall, Grace Work
2022 AWM Research Symposium
Women in Groups, Geometry, and Dynamics