Discrete Dynamics: Basic Theory and Examples

This book offers a complete and detailed introduction to the theory of  discrete dynamical systems, with special attention to stability of fixed  points and periodic orbits. It provides a solid mathematical background  and the essential basic knowledge for further developments such as, for  instance, deterministic chaos theory, for which many other references  are available (but sometimes, without an exhaustive presentation of  preliminary notions). Readers will find a discussion of topics sometimes  neglected in the research literature, such as a comparison between  different predictions achievable by the discrete time model and the  continuous time model of the same application. Another novel aspect of  this book is an accurate analysis of the way a fixed point may lose  stability, introducing and comparing several notions of instability:  simple instability, repulsivity, and complete instability. To help the  reader and to show the flexibility and potentiality of the discrete  approach to dynamics, many examples, numerical simulations, and figures  have been included. The book is used as a reference material for courses  at a doctoral or upper undergraduate level in mathematics and  theoretical engineering.