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Chaos Detection and Predictability

  • Charalampos (Haris) Skokos
  • Georg A. Gottwald
  • Jacques Laskar

Part of the Lecture Notes in Physics book series (LNP, volume 915)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Elena Lega, Massimiliano Guzzo, Claude Froeschlé
    Pages 35-54
  3. Georg A. Gottwald, Ian Melbourne
    Pages 221-247
  4. Stefan Siegert, Holger Kantz
    Pages 249-269
  5. Charalampos (Haris) Skokos, Georg A. Gottwald, Jacques Laskar
    Pages E1-E1

About this book

Introduction

Distinguishing chaoticity from regularity in deterministic dynamical systems and specifying the subspace of the phase space in which instabilities are expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics.

 

To address these issues there exists a plethora of methods for chaos detection and predictability. The most commonly employed technique for investigating chaotic dynamics, i.e. the computation of Lyapunov exponents, however, may suffer a number of problems and drawbacks, for example when applied to noisy experimental data.

 

In the last two decades, several novel methods have been developed for the fast and reliable determination of the regular or chaotic nature of orbits, aimed at overcoming the shortcomings of more traditional techniques. This set of lecture notes and tutorial reviews serves as an introduction to and overview of modern chaos detection and predictability techniques for graduate students and non-specialists.

 

The book covers theoretical and computational aspects of traditional methods to calculate Lyapunov exponents, as well as of modern techniques like the Fast (FLI), the Orthogonal (OFLI) and the Relative (RLI) Lyapunov Indicators, the Mean Exponential Growth factor of Nearby Orbits (MEGNO), the Smaller (SALI) and the Generalized (GALI) Alignment Index and the ‘0-1’ test for chaos.

Keywords

Chaos Detection and Phase Space Reconstruction Covariant and Finite Site Lyapunov Vectors Deterministic Dynamical Systems Fast and Relative Lyapunov Indicators Frequency Map Analysis Lyapunov Indicator Method MEGNO Method OFLI Method Recurrence Plots SALI and GALI Methods

Editors and affiliations

  • Charalampos (Haris) Skokos
    • 1
  • Georg A. Gottwald
    • 2
  • Jacques Laskar
    • 3
  1. 1.University of Cape TownDepartment of Mathematics and Applied MaRondeboschSouth Africa
  2. 2.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia
  3. 3.Observatoire de ParisIMCCEParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-48410-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2016
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-662-48408-1
  • Online ISBN 978-3-662-48410-4
  • Series Print ISSN 0075-8450
  • Series Online ISSN 1616-6361
  • Buy this book on publisher's site