Primož Škraba: Analyzing Dynamical Systems with Computational Topology

Abstract. Analyzing systems is a difficult problem that is often made much easier by a good choice of parametrization: a natural choice for dynamical systems is the mapping to the circle. This mapping can describe a variety of behaviour including (quasi)-periodicity and recurrence. This talk will introduce a topological approach for understanding dynamical systems from measurements. Starting with a time series measurement of a dynamical system, using a pipeline based in the framework of computational topology, we can recover an astonishing amount of information about the system. We begin by embedding the time series in a higher dimension and use persistent cohomology to construct a natural parameterization which makes further analysis much easier. The talk will not require a background in topology, but rather, I hope to illustrate how introducing topological information simplifies a number of application-specific problems, leading to simpler algorithms.