Analyzing Dynamical Systems with Computational Topology

03/24/2011 - 3:00pm
Primoz Skraba

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 under- standing dynamical systems from measurements. Starting with a time series measure- ment 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 coho- mology to construct a natural parameterization which makes further analysis much easier. I will discuss the individual components of the pipeline as well as show results on several examples of synthetic and real data.

Millikan 211 Pomona College
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