- KAM for PDEs
- Periodic and Quasi-periodic solutions of Hamiltonian PDEs
- Nonlinear wave and Schroedinger equations
- Reversible KAM theory
- KAM for unbounded perturbations: quasi linear KdV, derivative wave equations
- Water waves equations
- Birkhoff Lewis periodic orbits
- Almost periodic solutions
- Bifurcation Theory and Nash-Moser Implicit Function Theorems
- Birkhoff normal forms
- Variational and Topological Methods in the study of Hamiltonian systems
- Variational methods for periodic solutions
- Homoclinic and heteteoclinic solutions
- Dynamical systems
- Arnold Diffusion
- Chaotic dynamics
- Perturbation and Nekhoroshev Theory
- 3 body problem
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