On a conjecture for the critical behaviour of KAM tori.
On one approach to investigation of mechanical systems.
One-dimensional motion of balls.
Optimal stability and instability results for a class of nearly integrable Hamiltonian systems
We consider nearly integrable, non-isochronous, a-priori unstable Hamiltonian systems with a (trigonometric polynomial) -perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time by a variational method which does not require the existence of «transition chains of tori» provided by KAM theory. We also prove that our estimate of the diffusion time is optimal as a consequence of a general stability result proved via classical perturbation...