The topic of this book is the study of local and global bifurcations (qualitative changes in dynamics) of discrete-time maps as parameters are varied. It is divided into eleven chapters distributed in three parts.
Part 1 covers essentially all known theoretical results on bifurcations of maps, covering center manifold and normal form theory and codimension-one and -two bifurcations.
Part 2 covers software. In Chapter 5 numerical methods and algorithms are presented, while Chapter 6 discusses how these algorithms are implemented in the software package MatcontM. MatcontM is a software package written by the authors of this book which uses Matlab to perform bifurcation analysis of maps. Chapter 7 contains four tutorials on the use of MatcontM.
Part 3 contains four chapters, each devoted to the analysis of a particular map as a demonstration of the capabilities of MatcontM.
This book could be used as reference to known results on bifurcations of maps, or as a guide to the software MatcontM. It is clearly written and contains many high-quality figures.