Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems

Abstract

We consider the problem of Arnold's diffusion for nearly integrable isochronous Hamiltonian systems. We prove a shadowing theorem which improves the known estimates for the diffusion time. We also justify for three time scales systems that the splitting of the separatrices is correctly predicted by the Poincare'-Melnikov function.

7 pages

References in corpus (1)

• Pendulum: separatrix splitting

Cited by in corpus (5)

• Optimal stability and instability results for a class of nearly integrable Hamiltonian systems
• Asymptotic Expansion of the Homoclinic Splitting Matrix for the Rapidly, Quasiperiodically, Forced Pendulum
• Drift in phase space: a new variational mechanism with optimal diffusion time
• Fast Arnold Diffusion in three time scale systems
• Arnold's Diffusion in nearly integrable isochronous Hamiltonian systems