Michael C. Mackey: Chaos, Fractals, and Noise

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Cover: 9780387940496 | Chaos, Fractals, and Noise | Stochastic Aspects of Dynamics | Buch

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

This book gives 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 a variety of the sciences to illustrate the utility of the techniques presented. This material was organized and written to be accessible to scientists with knowledge of advanced calculus and differential equations. In various concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and chastic integrals and differential equations are introduced. The past few years have witnessed an explosive growth in interest in physical, biological, and economic systems that could be profitably studied using densities. Due to the general inaccessibility of the mathematical literature to the non-mathematician, there has been little diffusion of the concepts and techniques from ergodic theory into the study of these "chaotic" systems. This book intends to bridge that gap.

Erscheinungsjahr:	1993
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	492
Reihe:	Applied Mathematical Sciences
Inhalt:	xiv 474 S.
ISBN-13:	9780387940496
ISBN-10:	0387940499
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Mackey, Michael C. Lasota, Andrzej
Auflage:	2nd ed. 1994
Hersteller:	Springer US Springer New York Applied Mathematical Sciences
Maße:	241 x 160 x 31 mm
Von/Mit:	Michael C. Mackey (u. a.)
Erscheinungsdatum:	22.10.1993
Gewicht:	0,898 kg

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