Quantify the measure of initial data corresponding to stable motions (KAM tori) and the temporal scale for the appearance of possible macroscopic effects of instability (Nekhoroshev theory).
Explore three significant settings in which the study of billiards and billiard-like systems can be fruitfully exploited to tackle other problems; namely: Birkhoff conjecture and integrability of geodesic flows; refractive billiards and celestial mechanics; billiards and symplectic topology.
Investigate the dynamics and the stability properties of Hamiltonian dynamical systems governed by singular potentials, with a particular focus on the N-body problem and the N-centre problem in celestial mechanics, and the N-vortex problem in fluid dynamics and geophysics.
Extend the stability analysis developed in the framework of Hamiltonian systems to a broader class of systems that are important for real-world applications. We propose to focus on: conformally symplectic and almost symplectic systems, dissipative systems, and nonholonomic dynamics.