Grant: Alliance Grants

The goal of the present research is to understand better, and fully classify, a type of dynamical systems called Anosov and Pseudo-Anosov flows. Anosov flows are paradigmatic examples of chaotic dynamical systems, i.e., those systems where an arbitrarily small difference in initial condition leads to a large deviance in the behavior of the orbit, as popularized in the "butterfly effect". As such, understanding chaotic systems in general, and Anosov flows in particular, has been an important goal in the field of dynamical systems since at least the 1960s. In this proposal, we aim to tackle some of the biggest open questions surrounding pseudo-Anosov flows, such as obtaining a complete classification of these systems, understanding precisely which manifolds can carry such flows, and determining whether or not a given manifold can carry infinitely many non-equivalent pseudo-Anosov flows.