Hamiltonian systems instability resonances Arnold diffusion
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Pliska Studia Mathematica Bulgarica, Vol. 23, No 1, (2014), 189p-209p
We show the instability of action variables on resonant orbits of certain non-convex Hamiltonian systems with several degrees of freedom. Such orbits remain in the vicinity of resonant surfaces where the action variables can undergo changes O(1) infinitely often although the size of perturbations O(ε) can be arbitrarily small. We also perform numerical simulations to compare the effects of two condition for instability in two four-dimensional examples with random parameters. 2000 Mathematics Subject Classification: Primary 37J25, 37J40; Secondary 37C10, 37C40.