The Steep Nekhoroshev's Theorem

Revising Nekhoroshev's geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev's theorem for steep Hamiltonian systems proving, in particular, that the exponential stability exponent can be taken to be $1/ (2n α_1\cdotsα_{n-2}$) ($α_i$'s being Nekhoroshev's steepness indices and $n\ge 3$ the number of degrees of freedom).

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