Research

My research area is Hamiltonian Dynamical Systems.
  • Integrable Systems
    • Topology of Integrable Systems
    • Action-Angle variables, Hamiltonian Monodromy
    • Semiclassical quantization, Quantum Monodromy
    • KAM theory, Frequency Analysis and non-degeneracy conditions
    • semi-global symplectic invariants
  • Classical Mechanics
    • N-body problems
    • Rigid body dynamics
    • Non-rigid body dynamics in Biomechanics
    • Poisson structures
    • Geometric Phase
    • Symplectic and Poisson integrators
  • Bifurcation Theory
    • Twistless bifurcations
    • Hamiltonian Hopf Bifurcation
    • Resonances
  • Dynamics of Hamiltonian Maps
    • Symplectic maps
    • Billiards
    • Volume preserving maps
  • Symbolic Dynamics
    • SD in (ergodic) Billiards
    • SD in integrable systems
  • Euler Equations in Fluid Dynamics
    • Stability of equilibria on the torus
    • Zeitlin's Poisson structures
    • Global dynamics on the rotating sphere
  • PhD projects