Instabilities in Hamiltonian systems
Document typeMaster thesis
Rights accessOpen Access
In 1964, V. I. Arnol'd proved the existence of nearly-integrable Hamiltonian systems which have global instabilities (global chaotic behaviour). This phenomenon is nowadays termed under the name "Arnol'd diffusion". One of the key ideas that he used is to "travel" along invariant manifolds of the Hamiltonian system. The purpose of this project is to understand the Arnol'd instability mechanism and study new ones using different invariant objects.