Efficient Computation of Invariant Tori in Volume-Preserving Maps

Series: 
CDSNS Colloquium
Monday, August 26, 2013 - 16:00
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
Department of Mathematics, Georgia Institute of Technology
Volume preserving maps naturally arise in the study of many natural phenomena including incompressible fluid-flows, magnetic field-line flows, granular mixing, and celestial mechanics. Codimension one invariant tori play a fundamental role in the dynamics of these maps as they form boundaries to transport; orbits that begin on one side cannot cross to the other. In this talk I will present a Fourier-based, quasi-Newton scheme to compute the invariant tori of three-dimensional volume-preserving maps. I will further show how this method can be used to predict the perturbation threshold for their destruction and study the mechanics of their breakup.