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.