Arnold diffusion in nearly integrable Hamiltonian systems

In this paper, Arnold diffusion is proved to be generic phenomenon in nearly integrable convex Hamiltonian systems with three degrees of freedom: $H(x,y)=h(y)+εP(x,y), \qquad x\in\mathbb{T}^3,\ y\in\mathbb{R}^3.$ Under typical perturbation $εP$, the system admits "connecting" orbit that passes through any two prescribed small balls in the same energy level $H^{-1}(E)$ provided $E$ is bigger than the minimum of the average action, namely, $E>\minα$.

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