Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Stabilities and Instabilities in quasi-periodic Hamiltonian motions

Prof. Dr. Bassam Fayad talk

Speaker invited by: Prof. Dr. Artur Avila

**Date:** 05.11.18 **Time:** 15.30 - 16.30 **Room:** Y27H25

We introduce a new diffusion mechanism from the neighborhood of elliptic equilibria for Hamiltonian flows in three or more degrees of freedom. Using this mechanism, we obtain the first examples of real analytic Hamiltonians that have a Lyapunov unstable non-resonant elliptic equilibrium. We also give examples of real analytic invariant quasi-periodic tori of arbitrary frequency vectors that are Lyapunov unstable but have a polynomial Birkhoff normal form.