Asymptotic analysis of time singularities for a class of time-dependent Hamiltonians

Abstract

We analyse the local and global structure of time singularities for a class of quasi-integrable Hamiltonian systems in the Arnold - Liouville sense. We show that there is good agreement between the numerically observed local behaviour of the solutions and the perturbative scheme we produce using asymptotic approximations of the solution around the singularities. We also prove the convergence of the Psi-series associated to the movable singularities of the systems considered. We also propose a simple model in order to analyse the global structure of the singularities in the directions of exponential growth of the potential in time.