Overview

This book presents an exposition of recently discovered, unusual properties of difference equations. Even in the simplest scalar case, nonlinear difference equations have been proved to exhibit surprisingly varied and qualitatively different solutions. The latter can readily be applied to the modelling of complex oscillations and the description of the process of fractal growth and the resulting fractal structures. Difference equations give an elegant description of transitions to chaos and, also provide useful information on reconstruction inside chaos. In numerous simulations of relaxation and turbulence phenomena the difference equation description is therefore preferred to the traditional differential equation-based modelling. This monograph consists of four parts. The first part deals with one-dimensional dynamical systems, the second part treats nonlinear scalar difference equations of continuous argument. Parts three and four describe relevant applications in the theory of difference-differential equations and in the nonlinear boundary problems formulated for hyperbolic systems of partial differential equations. This text is intended not only for mathematicians but also for those interns and computer simulations of nonbiology and other fields.

Full Product Details

Author:   A.N. Sharkovsky ,  Y. L. Maistrenko ,  E.Yu Romanenko ,  P. V. Malyshev
Publisher:   Springer
Imprint:   Springer
Edition:   1993 ed.
Volume:   250
Dimensions:   Width: 15.50cm , Height: 2.20cm , Length: 23.50cm
Weight:   0.729kg
ISBN:  

9780792321941

ISBN 10:   0792321944
Pages:   358
Publication Date:   31 March 1993
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

I. One-Dimensional Dynamical Systems.- 1. Introduction to the Theory of Dynamical Systems.- 2. Periodic Trajectories.- 3. Behavior of Trajectories.- 4. Dynamical Systems for U-Maps.- II. Difference Equations with Continuous Time.- 1. Nonlinear Difference Equations.- 2. Difference Equations with U-Nonlinearity.- III. Differential-Difference Equations.- 1. Completely Integrable Differential-Difference Equations.- 2. Differential-Difference Equations Close To Difference Ones.- 3. Singularly Perturbed Differential-Difference Equations.- IV. Boundary-Value Problems for Hyperbolic Systems of Partial Differential Equations.- 1. Reduction of Boundary-Value Problems to Difference and Differential-Difference Equations.- 2. Boundary-Value Problem for a System with Small Parameter.- 3. Boundary-Value Problem for Systems with Two Spatial Variables.- References.

Reviews

' I enjoyed reading this book, and i am happy to recommend it to all those interested in finding out more about this fascinating but rather unfamiliar branch of dynamical systems.' Bulletin London Math. Soc. 27 1995

'I enjoyed reading this book, and i am happy to recommend it to all those interested in finding out more about this fascinating but rather unfamiliar branch of dynamical systems.' Bulletin London Math. Soc. 27 1995

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