Arnold Diffusion in Systems of \(n>3\) Degrees of Freedom

In this chapter, we give the proof of Theorems 7.1.2 , 7.1.3 and 7.1.4 for \(n>3\) based on our work [96]. This establishes the validity of the Arnold diffusion conjecture in the smooth category for convex Hamiltonians. The higher dimensional case is more relevant to the ergodic hypothesis than the \(n=3\) case as we have discussed in Chap. 7 .