This books combines an introductory survey of theory and techniques of discrete dynamical systems and difference equations with a manual for the use of the software package Dynamica. Many applications are presented as exercises and research projects. Dynamica, based on Mathematica, provides an easy-to-use collection of algebraic, numerical, and graphical tools and techniques that allow users to understand essential theoretical concepts quickly. The Dynamica package and notebooks corresponding to particular chapters are available for download from the internet.
Dynamics of One-Dimensional Dynamical Systems | Dynamics of Two-Dimensional Dynamical Systems | Systems of Difference Equations, Stability, and Semicycles | Invariants and Related Lyapunov Functions | Dynamics of Three-Dimensional Dynamical Systems | Fractals Generated by Iterated Function Systems
Calculus and Analysis