Speed of Arnold diffusion for analytic Hamiltonian systems

For a convex, real analytic, ε-close to integrable Hamiltonian system with n≥5 degrees of freedom, we construct an orbit exhibiting Arnold diffusion with the diffusion time bounded by exp(Ce^-frac12(n-2))exp(Cepsilon^{-frac{1}{2(n-2)}}). This upper bound of the diffusion time almost matches the lower bound of order exp(e^-frac12(n-1))exp(epsilon ^{-frac{1}{2(n-1)}}) predicted by the Nekhoroshev-type stability results. Our method is based on the variational approach of Bessi and Mather, and includes a new construction on the space of frequencies.