Dynamical Systems Seminar: Holger Dullin

Two Integrable Systems related to the Euler fluid equations on a rotating sphere

Holger Dullin

School of Mathematics and Statistics, The University of Sydney

Date and time: 

Thursday, February 19, 2015 - 2:00pm

Location: 

ECCR 257

Abstract: 

The Euler fluid equations on a rotating sphere can be projected to spherical harmonics with a Lie-Poisson structure of SU(N) using a construction due to Zeitlin. We will show that for N=3 and N=4 this gives integrable systems on the sphere of dimension N^2-1. The systems are super-integrable, can be integrated using a Lax pair, and have torus actions with a moment map whose image is a convex polytope.