Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics (Applied Mathematical Sciences)

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9780387940496: Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics (Applied Mathematical Sciences)

The first edition of this book was originally published in 1985 under the ti­ tle "Probabilistic Properties of Deterministic Systems. " In the intervening years, interest in so-called "chaotic" systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma­ turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe­ nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects. We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter.

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From the Back Cover:

In recent years there has been an explosive growth in the study of physical, biological, and economic systems that can be profitably studied using densities. Because of the general inaccessibility of the mathematical literature to the nonspecialist, little diffusion of the applicable mathematics into the study of these "chaotic" systems has taken place. This book will help bridge that gap. To show how densities arise in simple deterministic systems, the authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial-differential equations. Examples have been drawn from many fields to illustrate the utility of the concepts and techniques presented, and the ideas in this book should thus prove useful in the study of a number of applied sciences. The authors assume that the reader has a knowledge of advanced calculus and differential equations. Basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed. Physicists, chemists, and biomathematicians studying chaotic behavior will find this book of value. It will also be a useful reference or text for mathematicians and graduate students working in ergodic theory and dynamical systems.

Review:

"This is a truly outstanding book. It is so well and carefully written that, despite the complexity of the subject matte and the difficulty of some of the mathematics, virtually everything is completely clear on a first reading. Indeed, the book is much more absorbing than most novels." Probability in the Engineering + Informational Sciences

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Andrzej Lasota, Michael C. Mackey
Editorial: Springer-Verlag New York Inc., United States (1998)
ISBN 10: 0387940499 ISBN 13: 9780387940496
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Descripción Springer-Verlag New York Inc., United States, 1998. Hardback. Estado de conservación: New. 2nd ed. 1994. Corr. 3rd printing 1998. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. The first edition of this book was originally published in 1985 under the ti- tle Probabilistic Properties of Deterministic Systems. In the intervening years, interest in so-called chaotic systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma- turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe- nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects.We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter. Nº de ref. de la librería LIE9780387940496

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Descripción Springer-Verlag New York Inc., United States, 1998. Hardback. Estado de conservación: New. 2nd ed. 1994. Corr. 3rd printing 1998. Language: English . Brand New Book ***** Print on Demand *****.The first edition of this book was originally published in 1985 under the ti- tle Probabilistic Properties of Deterministic Systems. In the intervening years, interest in so-called chaotic systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma- turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe- nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects. We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter. Nº de ref. de la librería APC9780387940496

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Andrzej Lasota, Michael C. Mackey
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Descripción Springer-Verlag New York Inc., United States, 1998. Hardback. Estado de conservación: New. 2nd ed. 1994. Corr. 3rd printing 1998. Language: English . Brand New Book ***** Print on Demand *****. The first edition of this book was originally published in 1985 under the ti- tle Probabilistic Properties of Deterministic Systems. In the intervening years, interest in so-called chaotic systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma- turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe- nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects. We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter. Nº de ref. de la librería APC9780387940496

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