Passage Through Resonance

Abstract

In Chapter 7 we met a difficulty while applying straightforward averaging techniques to the problem at hand. We studied the case where this difficulty could not happen, that is, Ω0(x) does not vanish, calling this the regular case. We now return to the problem where Ω0 can have zeros or can be small. We cannot present a complete theory as such a theory is not available, so we rather aim at introducing the reader to the relevant concepts. This may serve as an introduction to the literature. In this context we mention [176, 125]; for the literature on passage of separatrices see [281]. To be more concrete, we will study the following equations.