Analyzing Dynamical Systems with Computational Topology

03/24/2011 - 3:00pm
03/24/2011 - 4:00pm
Speaker: 
Primoz Skraba (Jozef Stefan Institute, Ljubljana)
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 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.

Where: 
Millikan 211, Pomona College
Misc. Information: 

Refreshments served at 3:45 p.m. at Harry Mullikin Room, Millikan 209

The dinner will be hosted by Prof. Vin de Silva. If interested in attending, email vin.desilva@pomona.edu

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