Finding periodic orbits of (drilled) pseudo-Anosov flows

Anna Parlak
Max Planck Institute for Mathematics

Abstract

A (drilled) pseudo-Anosov flow admits a combinatorial description in terms of a finite directed graph, called the flow graph. Its bi-infinite directed paths encode orbits of the flow, with periodic paths corresponding to periodic orbits. I will explain how one can determine (in finitely many steps) the ambient isotopy classes of periodic orbits from their combinatorial description. This is joint work with Henry Segerman.