by Christian Mira (INSA Toulouse, France) , Laura Gardini (Istituto di Scienze Economiche Urbino, Italy) , Alexandra Barugola (Université de Provence Marseille, France) , & Jean-Claude Cathala (Université de Provence Marseille, France)

This book is essentially devoted to complex properties (Phase plane structure and bifurcations) of two-dimensional noninvertible maps, i.e. maps having either a non-unique inverse, or no real inverse, according to the plane point. They constitute models of sets of discrete dynamical systems encountered in Engineering (Control, Signal Processing, Electronics), Physics, Economics, Life Sciences. Compared to the studies made in the one-dimensional case, the two-dimensional situation remained a long time in an underdeveloped state. It is only since these last years that the interest for this research has increased. Therefore the book purpose is to give a global presentation of a matter, available till now only in a partial form. Fundamental notions and tools (such as “critical manifolds”), as the most part of results, are accompanied by many examples and figures.

• Generalities on Dynamics Systems and Maps
• One-Dimensional Noninvertible Maps
• Two-Dimensional Noninvertible Maps. Properties of Critical Curves
• Absorbing Areas and Chaotic Areas of Two-Dimensional Noninvertible Maps
• Basins and Their Bifurcations
• On Some Properties of Invariant Sets of Two-Dimensional Noninvertible Maps