Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Persistence of degenerate lower dimensional invariant tori in Hamiltonian systems

Talk by Dr. Frank Trujillo

**Date:** 05.10.20 **Time:** 15.00 - 16.15 **Room:** Y27H28

The classical KAM theory establishes the persistence, under sufficiently small perturbations, of most of the n-dimensional invariant tori of non-degenerate integrable Hamiltonians with n degrees of freedom. The surviving tori are those carrying a quasi-periodic motion by a Diophantine vector and, in particular, their restricted dynamics is minimal. On the other hand, such systems also admit n-dimensional invariant tori whose restricted dynamics is not minimal. These tori, which we call resonant, are foliated by invariant tori whose dimension is smaller than the number of degrees of freedom of the system. In this talk I will present a criterion for the persistence of at least one of the lower dimensional invariant tori associated to a resonant invariant torus.