Difference Equations and Their Applications: 250 (Mathematics and Its Applications) - Tapa blanda

Sharkovsky, A.N.; Maistrenko, Y. L.; Romanenko, E.Yu

 
9789401047746: Difference Equations and Their Applications: 250 (Mathematics and Its Applications)
Tapa blanda
ISBN 10: 940104774X ISBN 13: 9789401047746
Editorial: Springer, 2012

Sinopsis

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.

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Críticas

' 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

Reseña del editor

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.

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Editorial
Springer
Año de publicación
2012
Idioma
Inglés
ISBN 10 
940104774X
ISBN 13 
9789401047746
Encuadernación
Tapa blanda
Número de páginas
376
Contacto del fabricante
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Alemania

Otras ediciones populares con el mismo título

9780792321941: Difference Equations and Their Applications: 250 (Mathematics and Its Applications, 250)

Edición Destacada

ISBN 10:  0792321944 ISBN 13:  9780792321941
Editorial: Springer, 1993
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