Pseudo-Anosovs of interval type

Abstract 

A pseudo-Anosov (pA) is a homeomorphism of a compact connected surface S that, away from a finite set of points, acts locally as a linear map with one expanding and one contracting eigendirection. Ubiquitous yet mysterious, pAs have fascinated low-dimensional topologists and dynamicists for the past forty years. We show that any pA on the sphere whose associated quadratic differential has at most one zero, admits an invariant train track whose expanding subgraph is an interval. Concretely, such a pA has the dynamics of an interval map. As an application, we recover a uniform lower bound on the entropy of these pAs originally due to Boissy-Lanneau. Time permitting, we will also discuss potential applications to a question of Fried. This is joint work with Karl Winsor.

About the speaker 

I am a graduate student at Boston College, studying dynamics under Kathryn Lindsey. I am currently completing my dissertation.

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https://www.bc.edu/bc-web/schools/mcas/departments/math/people/grad-students/ethan-farber.html