Summary: Spectral theory is used to display instabilities and hyperbolic structure for certain periodic soliton equations, as well as to generate representations of whiskered tori for these equations. The NLS equation is discussed as a primary model, with references to other equations which possess a similar hyperbolic structure. This chapter in the theory of integrable soliton equations is described in the terminology of dynamical systems theory, in anticipation of its future use in the study of near integrable perturbations.
For the entire collection see [Zbl 0801.00009].