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 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
@article{RLIN_2000_9_11_4_a0,
     author = {Berti, Massimiliano and Bolle, Philippe},
     title = {Diffusion time and splitting of separatrices for nearly integrable isochronous {Hamiltonian} systems},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {235--243},
     year = {2000},
     volume = {Ser. 9, 11},
     number = {4},
     zbl = {1009.37044},
     mrnumber = {MR1837581},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2000_9_11_4_a0/}
}
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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/