Eric Fink (MSU) "Markov Partitions for Hyperbolic Automorphisms of Nilmanifolds"
- Monday, November 15, 2021 from 4:10pm to 5:15pm
- Wilson Hall, 1-143 - view map
Monday, November 15, 4:10-5:15pm MT
Wilson Hall 1-143
Eric Fink (Montana State University)
Markov Partitions for Hyperbolic Automorphisms of Nilmanifolds: Computational and Algorithmic Considerations
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.
- Department of Mathematical Sciences
406 994 3123