Niklas Brännström: Slow dynamics of a slow-fast Hamiltonian system

Hamiltonian dynamics is often used to model problems in
mathematical physics. In this talk we will focus on Hamiltonian systems with two time scales, that is, the system has a slow component and a fast component. Integrating the Hamiltonian equations of motion is a hard problem. A view that is often taken is that it is the slow dynamics that
represents the dynamics we are interested in while the fast component is just a perturbation (you may think of it as deterministic noise). Then using averaging techniques one may ( terms and conditions apply!) derive approximate slow dynamics. In this talk I will introduce a mechanism with
which (under suitable conditions) we can construct orbits which behaves quite differently from those predicted by the averaging theory. Colloquially, I will show a Hamiltonian "write-your-name theorem". This work has been done in collaboration with V.Gelfreich (Warwick) and E.
De Simone (Helsinki).