- Series
- CDSNS Colloquium
- Time
- Monday, October 1, 2012 - 4:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 06
- Speaker
- Adam Fox – Univ. of Colorado
- Organizer
- Rafael de la Llave
Invariant tori play a prominent role in the dynamics of symplectic
maps. These tori are especially important in two dimensional systems
where they form a boundary to transport. Volume preserving maps also
admit families of invariant rotational tori, which will restrict
transport in a d dimensional map with one action and d-1 angles. These
maps most commonly arise in the study of incompressible fluid flows,
however can also be used to model magnetic field-line flows, granular
mixing, and the perturbed motion of comets in near-parabolic orbits.
Although a wealth of theory has been developed describing tori in
symplectic maps, little of this theory extends to the volume preserving
case. In this talk we will explore the invariant tori of a 3
dimensional quadratic, volume preserving map with one action and two
angles. A method will be presented for determining when an invariant
torus with a given frequency is destroyed under perturbation, based on
the stability of approximating periodic orbits.