Advertisement

Analysis of Observed Chaotic Data

  • Henry D. I. Abarbanel

Part of the Institute for Nonlinear Science book series (INLS)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Henry D. I. Abarbanel
    Pages 1-12
  3. Henry D. I. Abarbanel
    Pages 13-23
  4. Henry D. I. Abarbanel
    Pages 25-37
  5. Henry D. I. Abarbanel
    Pages 39-67
  6. Henry D. I. Abarbanel
    Pages 69-93
  7. Henry D. I. Abarbanel
    Pages 95-114
  8. Henry D. I. Abarbanel
    Pages 115-132
  9. Henry D. I. Abarbanel
    Pages 133-145
  10. Henry D. I. Abarbanel
    Pages 147-172
  11. Henry D. I. Abarbanel
    Pages 173-215
  12. Henry D. I. Abarbanel
    Pages 217-235
  13. Henry D. I. Abarbanel
    Pages 237-247
  14. Back Matter
    Pages 249-272

About this book

Introduction

When I encountered the idea of chaotic behavior in deterministic dynami­ cal systems, it gave me both great pause and great relief. The origin of the great relief was work I had done earlier on renormalization group properties of homogeneous, isotropic fluid turbulence. At the time I worked on that, it was customary to ascribe the apparently stochastic nature of turbulent flows to some kind of stochastic driving of the fluid at large scales. It was simply not imagined that with purely deterministic driving the fluid could be turbulent from its own chaotic motion. I recall a colleague remarking that there was something fundamentally unsettling about requiring a fluid to be driven stochastically to have even the semblance of complex motion in the velocity and pressure fields. I certainly agreed with him, but neither of us were able to provide any other reasonable suggestion for the observed, apparently stochastic motions of the turbulent fluid. So it was with relief that chaos in nonlinear systems, namely, complex evolution, indistinguish­ able from stochastic motions using standard tools such as Fourier analysis, appeared in my bag of physics notions. It enabled me to have a physi­ cally reasonable conceptual framework in which to expect deterministic, yet stochastic looking, motions. The great pause came from not knowing what to make of chaos in non­ linear systems.

Keywords

Mathematica dynamical systems dynamics fractal geophysics information theory laser modeling noise physics stability

Authors and affiliations

  • Henry D. I. Abarbanel
    • 1
  1. 1.Institute for Nonlinear ScienceUniversity of California—San DiegoLa JollaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0763-4
  • Copyright Information Springer-Verlag New York Inc. 1996
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-98372-1
  • Online ISBN 978-1-4612-0763-4
  • Series Print ISSN 1431-4673
  • Buy this book on publisher's site