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Applied Mathematics Colloquium

Dr. Michael Jolly, Indiana University

Location

Mathematics/Psychology : 106

Date & Time

October 16, 2015, 11:30 am12:30 pm

Description

Title: Dimension reduction and explosion

Abstract: We start by defining some basic notions from dynamical systems, culminating with that of an inertial manifold. The restriction of a flow to such a manifold can reduce an infinite dimensional system to a finite set of ordinary differential equations which captures all the long time behavior. We then move to the related notion of a foliation of phase space consisting of a pair manifolds at each point. Finally, we consider the case where such a reduction is not known to be possible, and instead derive an ODE in a Banach space of trajectories in which those on the attractor are readily identified.