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  • Textbook
  • © 1994

Chaos, Fractals, and Noise

Stochastic Aspects of Dynamics

Part of the book series: Applied Mathematical Sciences (AMS, volume 97)

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  • ISBN: 978-1-4612-4286-4
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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xiv
  2. Introduction

    • Andrzej Lasota, Michael C. Mackey
    Pages 1-15
  3. The Toolbox

    • Andrzej Lasota, Michael C. Mackey
    Pages 17-36
  4. Markov and Frobenius-Perron Operators

    • Andrzej Lasota, Michael C. Mackey
    Pages 37-50
  5. Studying Chaos with Densities

    • Andrzej Lasota, Michael C. Mackey
    Pages 51-84
  6. The Asymptotic Properties of Densities

    • Andrzej Lasota, Michael C. Mackey
    Pages 85-137
  7. The Behavior of Transformations on Intervals and Manifolds

    • Andrzej Lasota, Michael C. Mackey
    Pages 139-188
  8. Continuous Time Systems: An Introduction

    • Andrzej Lasota, Michael C. Mackey
    Pages 189-249
  9. Discrete Time Processes Embedded in Continuous Time Systems

    • Andrzej Lasota, Michael C. Mackey
    Pages 251-281
  10. Entropy

    • Andrzej Lasota, Michael C. Mackey
    Pages 283-301
  11. Stochastic Perturbation of Discrete Time Systems

    • Andrzej Lasota, Michael C. Mackey
    Pages 303-334
  12. Stochastic Perturbation of Continuous Time Systems

    • Andrzej Lasota, Michael C. Mackey
    Pages 335-392
  13. Markov and Foias Operators

    • Andrzej Lasota, Michael C. Mackey
    Pages 393-447
  14. Back Matter

    Pages 449-474

About this 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.

Keywords

  • Ergodic theory
  • Markov process
  • Probability theory
  • measure theory
  • partial differential equation

Reviews

"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

Authors and Affiliations

  • Institute of Mathematics, Silesian University, Katowice, Poland

    Andrzej Lasota

  • Center of Nonlinear Dynamics, McGill University, Montreal, Canada

    Michael C. Mackey

Bibliographic Information

  • Book Title: Chaos, Fractals, and Noise

  • Book Subtitle: Stochastic Aspects of Dynamics

  • Authors: Andrzej Lasota, Michael C. Mackey

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4612-4286-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1994

  • Hardcover ISBN: 978-0-387-94049-6

  • Softcover ISBN: 978-1-4612-8723-0

  • eBook ISBN: 978-1-4612-4286-4

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 2

  • Number of Pages: XIV, 474

  • Additional Information: Originally published by Cambridge University Press, Cambridge, 1985

  • Topics: Probability Theory, Complex Systems, Theoretical, Mathematical and Computational Physics

Buying options

eBook USD 79.99
Price excludes VAT (USA)
  • ISBN: 978-1-4612-4286-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 99.99
Price excludes VAT (USA)
Hardcover Book USD 139.99
Price excludes VAT (USA)