Christian Mira

Contents: Dynamical Systems and Recurrences. GeneralitiesSome Properties of One-Dimensional Recurrences (Maps)Myrberg's Results on the One-Dimensional Quadratic Recurrences. Their ConsequencesThe Box-Within-a-Box Bifurcations Structure and Its ConsequencesSome Properties of Two-Dimensional Recurrences (Maps)Two-Dimensional Diffeomorphisms and the Foliated Box-Within-a-Box Bifurcations Structureand other papers Readership: Applied mathematicians, engineers and other physicists. Keywords:Endomorphism;Diffeomorphism;Recurrences;Bifurcations Structure

Chaotic Dynamics: From The One-dimensional Endomorphism To The Two-dimensional Diffeomorphism

Ralph Abraham

Laura Gardini

The materials in the book and on the accompanying disc are not solely developed with only the researcher and professional in mind, but also with consideration for the student: most of this material has been class-tested by the authors. The book is packed with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-colour animations tied directly to the subject matter of the book itself. The cross-platform CD also contains the program ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided to allow readers to work directly with the code from which the graphics in the book were taken.

A Visual Introduction in 2 Dimensions

Chaos in Discrete Dynamical Systems

Alexandra Barugola

Jean-Claude Cathala

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:Generalities on Dynamics Systems and MapsOne-Dimensional Noninvertible MapsTwo-Dimensional Noninvertible Maps. Properties of Critical CurvesAbsorbing Areas and Chaotic Areas of Two-Dimensional Noninvertible MapsBasins and Their BifurcationsOn Some Properties of Invariant Sets of Two-Dimensional Noninvertible Maps Readership: Nonlinear scientists, engineers and physicists. keywords:Noninvertible Maps;Multiple Preimages;Critical Curves;Plane Foliation;Absorbing Areas;Chaotic Areas;Invariant Sets;Disconnected Basins;Multiplyconnected Basins;Bifurcations involving Critical Sets

Christian Mira

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