Chaotic Dynamics in Two-dimensional Noninvertible Maps (World Scientific Series on Nonlinear Science Series a)

Barugola, Alexandra/ Cathala, Jean-claude/ Gardini, Laura

World Scientific Publishing Co Pte Ltd（1996/07発売）

• 製本 Hardcover:ハードカバー版／ページ数 632 p.
• 言語 ENG
• 商品コード 9789810216474
• DDC分類 515.35

Full Description

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.

Contents

Part 1: Generalities and definition; one-dimensional endomorphisms; the simplest type of two-dimensional endomorphisms. Part 2: Properties of the phase plane; simplest type of two-dimensional endomorphisms. Part 3: Bifurcations; more complex types of two-dimensional endomorphisms; generalizations to higher dimensions.