Geometric and numerical approaches to non-twist KAM theory
主 题: Geometric and numerical approaches to non-twist KAM theory
报告人: Rafael de la Llave (Professor. Georgia Tech. )
时 间: 2014-07-04 15:00-16:00
地 点: 理科一号楼1303（主持人：柳彬）
It is widely believed in the plasma physics and in the oceanography community that KAM tori whose Birkhoff normal forms are degenerate are very effective barriers to "transport", so that non-twist KAM tori have become a design goal in plasma confinement machines.
We present a systematic theory of the persistence of these objects in families with enough parameters (these will be the design parameters for the confinement machine). The degeneracy of the Birkhoff Normal form is quantified using Singularity theory and the persistence is obtained using KAM theory.
The method of proof leads also to very efficient algorithms which we have implemented in some cases. We will also present some numerical results.