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Chaos, Fractals, and Noise

Stochastic Aspects of Dynamics

  • Andrzej Lasota
  • Michael C. Mackey

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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Andrzej Lasota, Michael C. Mackey
    Pages 1-15
  3. Andrzej Lasota, Michael C. Mackey
    Pages 17-36
  4. Andrzej Lasota, Michael C. Mackey
    Pages 37-50
  5. Andrzej Lasota, Michael C. Mackey
    Pages 51-84
  6. Andrzej Lasota, Michael C. Mackey
    Pages 85-137
  7. Andrzej Lasota, Michael C. Mackey
    Pages 139-188
  8. Andrzej Lasota, Michael C. Mackey
    Pages 189-249
  9. Andrzej Lasota, Michael C. Mackey
    Pages 251-281
  10. Andrzej Lasota, Michael C. Mackey
    Pages 283-301
  11. Andrzej Lasota, Michael C. Mackey
    Pages 303-334
  12. Andrzej Lasota, Michael C. Mackey
    Pages 335-392
  13. Andrzej Lasota, Michael C. Mackey
    Pages 393-447
  14. Back Matter
    Pages 449-474

About this book

Introduction

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

Authors and affiliations

  • Andrzej Lasota
    • 1
  • Michael C. Mackey
    • 2
  1. 1.Institute of MathematicsSilesian UniversityKatowicePoland
  2. 2.Center of Nonlinear DynamicsMcGill UniversityMontrealCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4286-4
  • Copyright Information Springer-Verlag New York 1994
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8723-0
  • Online ISBN 978-1-4612-4286-4
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • Buy this book on publisher's site
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