Chaos and Non-Integrability of Hamiltonian  Systems (KAM Theorem)

The aim of this project was to explore the main properties of a symplectic phase space in relation to conservative Hamiltonian systems. It is found that, because of the symplectic nature of the phase space, any Hamiltonian system that has $n$ constants of the motion that are all in involution is integrable, i.e. that it is possible to obtain a closed-form solution.
The consequences of adding a perturbative term that renders the Hamiltonian system non-integrable are also discussed. The KAM theorem is exemplified through the famed Henon potential, though it is not proven.
The (French) paper is available here.