Invariant objects and Arnold diffusion. From theory to computation.

Research Horizons Seminar
Wednesday, March 4, 2020 - 12:20pm for 1 hour (actually 50 minutes)
Skiles 005
Rafael de la Llave – Georgia Tech
Skye Binegar

We consider the problem whether small perturbations of integrable mechanical systems can have very large effects.

Since the work of Arnold in 1964, it is known that there are situations where the perturbations can accumulate (Arnold diffusion). 

This can be understood by noting that the small perturbations generate some invariant objects in phase space that act as routes which allow accumulation of effects. 

We will present some rigorous results about geometric objects lead to Arnold diffusion as well as some computational tools that allow to find them in concrete applications.

Thanks to the work of many people, an area which used to be very speculative, is becoming an applicable tool.