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Difference Equations and Their Applications

  • A. N. Sharkovsky
  • Yu. L. Maistrenko
  • E. Yu. Romanenko

Part of the Mathematics and Its Applications book series (MAIA, volume 250)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Introduction

    1. A. N. Sharkovsky, Yu. L. Maistrenko, E. Yu. Romanenko
      Pages 1-13
  3. One-Dimensional Dynamical Systems

    1. A. N. Sharkovsky, Yu. L. Maistrenko, E. Yu. Romanenko
      Pages 15-43
    2. A. N. Sharkovsky, Yu. L. Maistrenko, E. Yu. Romanenko
      Pages 45-70
    3. A. N. Sharkovsky, Yu. L. Maistrenko, E. Yu. Romanenko
      Pages 71-94
    4. A. N. Sharkovsky, Yu. L. Maistrenko, E. Yu. Romanenko
      Pages 95-124
  4. Difference Equations with Continuous Time

    1. A. N. Sharkovsky, Yu. L. Maistrenko, E. Yu. Romanenko
      Pages 125-158
    2. A. N. Sharkovsky, Yu. L. Maistrenko, E. Yu. Romanenko
      Pages 159-185
  5. Differential-Difference Equations

    1. Front Matter
      Pages 187-187
    2. A. N. Sharkovsky, Yu. L. Maistrenko, E. Yu. Romanenko
      Pages 188-222
    3. A. N. Sharkovsky, Yu. L. Maistrenko, E. Yu. Romanenko
      Pages 223-237
    4. A. N. Sharkovsky, Yu. L. Maistrenko, E. Yu. Romanenko
      Pages 239-272
  6. Boundary-Value Problems for Hyperbolic Systems of Partial Differential Equations

    1. Front Matter
      Pages 273-273
    2. A. N. Sharkovsky, Yu. L. Maistrenko, E. Yu. Romanenko
      Pages 274-284
    3. A. N. Sharkovsky, Yu. L. Maistrenko, E. Yu. Romanenko
      Pages 285-304
    4. A. N. Sharkovsky, Yu. L. Maistrenko, E. Yu. Romanenko
      Pages 305-334
  7. Back Matter
    Pages 335-358

About this book

Introduction

The theory of difference equations is now enjoying a period of Renaissance. Witness the large number of papers in which problems, having at first sight no common features, are reduced to the investigation of subsequent iterations of the maps f· IR. m ~ IR. m, m > 0, or (which is, in fact, the same) to difference equations The world of difference equations, which has been almost hidden up to now, begins to open in all its richness. Those experts, who usually use differential equations and, in fact, believe in their universality, are now discovering a completely new approach which re­ sembles the theory of ordinary differential equations only slightly. Difference equations, which reflect one of the essential properties of the real world-its discreteness-rightful­ ly occupy a worthy place in mathematics and its applications. The aim of the present book is to acquaint the reader with some recently discovered and (at first sight) unusual properties of solutions for nonlinear difference equations. These properties enable us to use difference equations in order to model complicated os­ cillating processes (this can often be done in those cases when it is difficult to apply ordinary differential equations). Difference equations are also a useful tool of syn­ ergetics- an emerging science concerned with the study of ordered structures. The application of these equations opens up new approaches in solving one of the central problems of modern science-the problem of turbulence.

Keywords

chaos dynamical systems dynamische Systeme linearity modeling partial differential equation simulation

Authors and affiliations

  • A. N. Sharkovsky
  • Yu. L. Maistrenko
  • E. Yu. Romanenko
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKievUkraine

Bibliographic information