Melnikov’s method and Arnold diffusion for perturbations of integrable Hamiltonian systems a)
Melnikov’s method and Arnold diffusion for perturbations of integrable Hamiltonian systems a)
We start with an unperturbed system containing a homoclinic orbit and at least two families of periodic orbits associated with action angle coordinates. We use Kolmogorov–Arnold–Moser (KAM) theory to show that some of the resulting tori persist under small perturbations and use a vector of Melnikov integrals to show that, …