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Difference Equations and Their Applications : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - A.N. Sharkovskii

Difference Equations and Their Applications



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  • Paperback View Product Published: 29th October 2012

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, furthermore, 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. The book is intended not only for mathematicians but also for those interested in mathematical applications and computer simulations of nonlinear effects in physics, chemistry, biology and other fields.

' 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

Introductionp. 1
One-Dimensional Dynamical Systemsp. 15
Introduction to the Theory of Dynamical Systemsp. 15
Periodic Trajectoriesp. 45
Behavior of Trajectoriesp. 71
Dynamical Systems for U-Mapsp. 95
Difference Equations with Continuous Timep. 125
Nonlinear Difference Equationsp. 125
Difference Equations with U-Nonlinearityp. 159
Differential-Difference Equationsp. 187
Completely Integrable Differential-Difference Equationsp. 188
Differential-Difference Equations Close To Difference Onesp. 223
Singularly Perturbed Differential-Difference Equationsp. 239
Boundary-Value Problems for Hyperbolic Systems of Partial Differential Equationsp. 273
Reduction of Boundary-Value Problems to Difference and Differential-Difference Equationsp. 274
Boundary-Value Problem for a System with Small Parameterp. 285
Boundary-Value Problem for Systems with Two Spatial Variablesp. 305
Referencesp. 335
Indexp. 357
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792321941
ISBN-10: 0792321944
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 358
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 17.15  x 1.91
Weight (kg): 0.82