Revising Nekhoroshev’s geometry of resonances, we provide a fully con- structive and quantitative proof of Nekhoroshev’s theorem for steep Hamiltonian sys- tems proving, in particular, that the exponential stability exponent can be taken to be 1/(2nα_1··α_(n−2))(αi ’s being Nekhoroshev’s steepness indices and n≥3 the number of degrees of freedom). On the base of a heuristic argument, we conjecture that the new stability exponent is optimal.
The Steep Nekhoroshev’s Theorem
GUZZO, MASSIMILIANO;CHIERCHIA, LUIGI;BENETTIN, GIANCARLO
2016
Abstract
Revising Nekhoroshev’s geometry of resonances, we provide a fully con- structive and quantitative proof of Nekhoroshev’s theorem for steep Hamiltonian sys- tems proving, in particular, that the exponential stability exponent can be taken to be 1/(2nα_1··α_(n−2))(αi ’s being Nekhoroshev’s steepness indices and n≥3 the number of degrees of freedom). On the base of a heuristic argument, we conjecture that the new stability exponent is optimal.
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