Basic Definitions and Notions

The notion of slow-fast family on an arbitrary surface, as used throughout the book, is introduced in an intrinsic way. Examples are given to display the variation of situations that is dealt with, as well as examples that are beyond the scope of the book. Attention also goes to the more common and more restricted definitions. The chapter ends by stressing the big difference between singular points that are normally hyperbolic and the other ones, that are called contact points.