Dr. Eric Fink (Montana State University)

11/15/2021  4:10pm

 

Abstract: 

A celebrated result by Sinai (subsequently extended by Bowen) gives the existence of a Markov partition and associated conjugate symbolic dynamical system for any Anosov diffeomorphism on a compact manifold. Our recent work with Prof. Kwapisz provides an explicit construction in the setting of nilmanifolds (conjecturally the most general setting, up to a finite covering). Just as there is a philosophical gap between an existence proof and an explicit construction, there is again a gap between an explicit construction and a computationally tractable algorithm. In this talk, we will explore how these gaps were filled (e.g., optimizing Thurston's Solitaire; Hopcroft's and Brzozowski's Algorithms) by means of motivated (non-)examples, including irrational base expansions of the real numbers and hyperbolic toral automorphisms.