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Primož Škraba: Analyzing Dynamical Systems with Computational Topology

Date: 4. 5. 2011
Source: Graph theory and algorithms seminar
Četrtek 5. 5. 2011 ob 12:15 v predavalnici 3.05 na Jadranski 21.
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.