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Dynamical Systems and PDEs

  • 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
    • Long time existence results for quasi-linear Hamiltonian PDEs
    • Paradifferential 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
  • Benjamin-Feir and modulational instability
Research Group: 
Mathematical Analysis, Modelling, and Applications

Dynamics of nonlinear PDEs

We shall discuss the complex dynamics of Hamiltonian or reversible PDEs, like the NLS,  the Klein-Gordon equation, the wave equation in several dimension,the water waves equations of hydrodynamics, focusing on both chatotic and regular behaviour as the existence of quasi-periodic solutions.We shall discuss also long time existence results obtained by Birkhoff normal forms.

Dynamical Systems and PDEs

Research topics

  • KAM for PDEs
  • Water waves, KdV, Schrödinger and Klein-Gordon equations
  • Hamiltonian systems
  • Birkhoff normal form for PDEs and long time existence
    • Long time existence results for quasi-linear Hamiltonian PDEs
    • Paradifferential normal forms
  • Chaotic Dynamics and Arnold Diffusion
  • Variational Methods
  • Perturbative Methods in Critical Point Theory
  • Benjamin-Feir and modulational instability

Research Group

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