Feb 17, 2017

James Muldowney

University of Alberta, Department of Mathematical and Statistical Sciences

3:00 pm in MSB 318 (Math Colloquium)

Evolution of k-surfaces in dynamics

The evolution of curves in the dynamical system of a differential equation is usually studied using the linearized equation. If the system is n-dimensional, the evolution of n- dimensional volumes is governed by the scalar Liouville equation. We will examine equations that are associated with the evolution of k-dimensional surfaces, 1 ≤ k ≤ n, and look at the implications of these for the dynamics. This involves the use of additive and multiplicative kth-compound matrices which have some intrinsic interest for their metric and algebraic properties.