Sinossi
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.
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Recensione
' 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
Contenuti
Notation. Preface. Introduction. Part 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. Part II: Difference Equations with Continuous Time. 1. Nonlinear Difference Equations. 2. Difference Equations with U Nonlinearity. Part III: Differential-Difference Equations. 1. Completely Integrable Differential-Difference Equations. 2. Differential-Difference Equations close to Difference Ones. 3. Singularly Perturbed Differential-Difference Equations. Part 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 System with Two Spatial Variables. References. Index.
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Difference Equations and Their Applications
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Springer Netherlands Mrz 1993, 1993
ISBN 10: 0792321944
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 376 pp. Englisch. Codice articolo 9780792321941
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Buch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 376 pp. Englisch. Codice articolo 9780792321941
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Codice articolo 9780792321941
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