Mathematics Colloquium: Periodic data rigidity of Anosov diffeomorphisms

Speaker:  Jonathan DeWitt, University of Maryland

Title:  Periodic data rigidity of Anosov diffeomorphisms

Abstract :  Anosov diffeomorphisms are a class of dynamical systems that exhibit strong chaotic behavior. As such, they are central examples in the field of dynamical systems. However, after their introduction it was quickly understood that Anosov diffeomorphisms have strong rigidity properties: they seem to exist on few manifolds. Further, every known Anosov diffeomorphism is topologically equivalent to a ``linear" Anosov diffeomorphism, which comes from a simple algebraic construction. Consequently, there is a finer question as well: when are two Anosov diffeomorphisms that are equivalent as homeomorphisms also equivalent as diffeomorphisms? The study of periodic data rigidity seeks to provide one answer to this question. In this talk we will discuss periodic data rigidity and, in particular, discuss a recent joint result with Andrey Gogolev on global periodic data rigidity of Anosov diffeomorphisms. 

Time:  Friday, October 27, 3:30pm – 4:20pm

Place:  Exploratory Hall, room 4106

Zoom and In-person