ABSTRACT
Many interesting problems of Physics, like for instance those arising in Celestial Mechanics, can be represented as small perturbations of integrable systems. Small perturbations of integrable systems transform them into quasi-integrable systems, and their study is the subject of Hamiltonian Perturbation Theory. In the framework of Hamiltonian systems, a remarkable exception corresponds to mechanical systems which are integrable in the sense of Liouville-Arnold. In this chapter, the authors introduce the Hamiltonian model and the symplectic mapping that they have studied and describe the expected phenomenology of the motions in the Arnold web. They provide the definition of the Fast Lyapunov Indicator and give a simple example of applications on some characteristic orbits of the mapping. The authors show how the Arnold web evolves in the transition from order to chaos for both the Hamiltonian model and the symplectic mapping. They present results on the Arnold web.
