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The main result says that for a \"generic\" perturbation of a nearly integrable system of arbitrary degrees of freedom $n\\ge 2$ \\[ H_0(p)+\\eps H_1(\\th,p,t),\\quad \\th\\in \\T^n,\\ p\\in B^n,\\ t\\in \\T=\\R/\\T, \\] with strictly convex $H_0$ there exists an orbit $(\\th_{\\e},p_{e})(t)$ exhibiting Arnold diffusion in the sens that [\\sup_{t>0}\\|p(t)-p(0) \\| >l(H_1)>0] where $l(H_1)$ is a positive constant independant of $\\e$.\n  Our proof is a combination of geometric and variational methods. 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