Eric Fink (MSU): “Markov Partition for a Six-Dimensional Anosov Nilmanifold Diffeomorphism“
- Monday, November 19, 2018 from 4:00pm to 5:00pm
- Wilson Hall, 1-144 - view map
A classical result by Sinai and Bowen asserts existence of a Markov partition for any Anosov diffeomorphism on a compact manifold. In this talk, we will discuss a method to explicitly and efficiently construct a Markov partition and the associated symbolic dynamical system for a specific algebraic Anosov diffeomorphism on a six-dimensional nilmanifold. The method should extend to any algebraic Anosov diffeomorphism carried by a nilmanifold or an infra-nilmanifold. (A longstanding open conjecture asserts that any Anosov diffeomorphisms is such, up to conjugacy.) Our approach builds upon the work done in the 1990s for the case of hyperbolic toral automorphisms (especially that of Kenyon, Le Borgne, and Vershik).
- Department of Mathematical Sciences