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.
