July  2002, 8(3): 795-811. doi: 10.3934/dcds.2002.8.795

Fast Arnold diffusion in systems with three time scales

1. 

S.I.S.S.A., Via Beirut 2-4, 34014 Trieste, Italy

2. 

Département de mathématiques, Université d'Avignon, 33, rue Louis Pasteur, 84000 Avignon, France

Received  April 2001 Revised  August 2001 Published  April 2002

We consider the problem of Arnold Diffusion for nearly integrable partially isochronous Hamiltonian systems with three time scales. By means of a careful shadowing analysis, based on a variational technique, we prove that, along special directions, Arnold diffusion takes place with fast (polynomial) speed, even though the "splitting determinant" is exponentially small.
Citation: Massimiliano Berti, Philippe Bolle. Fast Arnold diffusion in systems with three time scales. Discrete & Continuous Dynamical Systems - A, 2002, 8 (3) : 795-811. doi: 10.3934/dcds.2002.8.795
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