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A hybrid method for computing Lyapunov exponents

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Abstract

In this paper we propose a numerical method for computing all Lyapunov coefficients of a discrete time dynamical system by spatial integration. The method extends an approach of Aston and Dellnitz (Comput Methods Appl Mech Eng 170:223–237, 1999) who use a box approximation of an underlying ergodic measure and compute the first Lyapunov exponent from a spatial average of the norms of the Jacobian for the iterated map. In the hybrid method proposed here, we combine this approach with classical QR-oriented methods by integrating suitable R-factors with respect to the invariant measure. In this way we obtain approximate values for all Lyapunov exponents. Assuming somewhat stronger conditions than those of Oseledec’ multiplicative theorem, these values satisfy an error expansion that allows to accelerate convergence through extrapolation.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501, Bielefeld, Germany

    Wolf-Jürgen Beyn & Alexander Lust

Authors
  1. Wolf-Jürgen Beyn
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  2. Alexander Lust
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Correspondence to Wolf-Jürgen Beyn.

Additional information

W.-J. Beyn and A. Lust was supported by CRC 701 ‘Spectral Analysis and Topological Methods in Mathematics’. The paper is mainly based on the PhD thesis [27] of A. Lust.

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Beyn, WJ., Lust, A. A hybrid method for computing Lyapunov exponents. Numer. Math. 113, 357–375 (2009). https://doi.org/10.1007/s00211-009-0236-4

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  • DOI: https://doi.org/10.1007/s00211-009-0236-4

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