This chapter describes forcing relations, different diffusion mechanisms, and Aubry-Mather types. The Aubry set can be decomposed into disjoint invariant sets called static classes, which gives important insight into the structure of the Aubry set. The chapter then formulates Theorem 2.2 and shows that it implies the book's main theorem. It utilizes the concept of forcing equivalence. The actual definition is not important for the current discussions, instead, the chapter states its main application to Arnold diffusion. The chapter also looks at symplectic coordinate changes. The definition of exact symplectic coordinate change for a time-periodic system is somewhat restrictive, and in particular, it does not apply directly to the linear coordinate change performed at the double resonance.
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