A.N. Sharkovsky – författare
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4 produkter
1 068 kr
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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.
537 kr
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The theory of one-dimensional systems is an efficient tool in nonlinear dynamics. On the one hand, it describes one-dimensional systems fairly completely, and on the other hand exhibits all basic complicated nonlinear effects. This volume acquaints the reader with the fundamentals of the theory of one-dimensional dynamical systems. Very simple nonlinear maps with a single point of extremum, also called unimodal maps, are studied. Unimodal is found to impose hardly any restrictions on the dynamical behaviour. It also provides a view of the problems appearing in the theory of dynamical systems. and describes the methods used for their solution in the case of one-dimensional maps. The book should be of interest to researchers and postgraduate students whose work involves nonlinear dynamics.
538 kr
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The theory of one-dimensional systems is one of the most efficient tools of nonlinear dynamics, as, on the one hand, it describes one-dimensional systems fairly completely, and on the other hand exhibits all basic complicated nonlinear effects. This volume has two main goals. Firstly, it acquaints the reader with the fundamentals of the theory of one-dimensional dynamical systems. Very simple nonlinear maps with a single point of extremum, also called unimodal maps, are studied. Unimodality is found to impose hardly any restrictions on the dynamical behaviour. Secondly, it equips the reader with a comprehensive view of the problems appearing in the theory of dynamical systems and describes the methods used for their solution in the case of one-dimensional maps. Audience: This book will be of interest to researchers and postgraduate students whose work involves nonlinear dynamics.
1 069 kr
Skickas inom 10-15 vardagar
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.