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

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

2000-09-19

arxiv.org/abs/math/0009176v1

Mathematics

Dynamical Systems

7 pages

Scientific paper

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.

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