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In this book we will study equations of the following form x= f (x, t; µ),(0.0. 1) and x↦→ g (x; µ),(0.0. 2) with x∈ U⊂ Rn, t∈ R1, and µ∈ V⊂ Rp where U and V are open sets in Rn and Rp, respectively. The overdot in (0.0. 1) means “d dt

,” and we view the variables µ as parameters. In the study of dynamical systems the independent variable is often referred to as “time.” We will use this terminology from time to time also. We refer to (0.0. 1) as a vector field or ordinary differential equation and to (0.0. 2) as a map or difference equation. Both will be termed dynamical systems. Before discussing what we might want to know about (0.0. 1) and (0.0. 2), we need to establish a bit of terminology.