Geodesic
Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 11 (2000) no. 4, pp. 235-243.

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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 Poincaré-Melnikov function.
Consideriamo il problema della diffusione di Arnold per sistemi Hamiltoniani isocroni quasi-integrabili. Dimostriamo un teorema di shadowing che migliora le stime sul tempo di diffusione sinora note. Giustifichiamo inoltre, per sistemi a tre scale temporali, che lo splitting delle separatrici è correttamente previsto dalla funzione di Poincaré-Melnikov. 
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Berti, Massimiliano; Bolle, Philippe. Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 11 (2000) no. 4, pp. 235-243. http://geodesic.mathdoc.fr/item/RLIN_2000_9_11_4_a0/

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