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. I will discuss the individual components of the pipeline as well as show results on several examples of synthetic and real data. the analyses of communicating virtual machines running unmodified, even closed-source binaries.

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