Geometric singular perturbation theory beyond the standard form

Martin Wechselberger (May 7, 2020)

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In this talk I will review geometric singular perturbation theory, but with a twist— I focus on a coordinate-independent setup of the theory. The need for such a theory beyond the standard form is motivated by looking at biochemical reaction, electronic and mechanical oscillator models that show relaxation-type behaviour. While the corresponding models incorporate slow and fast processes leading to multiple time-scale dynamics, not all of these models take globally the form of a standard slow–fast system. Thus from an application point of view, it is desirable to provide tools to analyse singularly perturbed systems in a coordinate-independent manner.