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Lyapunov Exponents

  • Juan C. Vallejo
  • Miguel A. F. Sanjuan
Chapter
Part of the Springer Series in Synergetics book series (SSSYN)

Abstract

Lyapunov exponents are a well-known diagnostic tool for analysing the presence of chaos in a system. They provide a quantitative measure of the divergence or convergence of nearby trajectories, by averaging the expansion rate of the phase space. In practice, the calculation is performed numerically and a finite-time integration time is used instead of the necessary infinite time. Moreover, the convergence of the averaging process towards the final asymptotic value can be very long. The distributions of finite-time Lyapunov exponents exploit the dependence on the finite-time for tracing the dynamics of the flow, and by analysing how their shapes change, we get insight into the specific nature of the orbit.

Keywords

Lyapunov Exponent Interval Size Lyapunov Spectrum Distortion Tensor Lyapunov Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Juan C. Vallejo
    • 1
  • Miguel A. F. Sanjuan
    • 1
  1. 1.Department of PhysicsUniversidad Rey Juan CarlosMóstoles, MadridSpain

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