Error analysis of a hybrid method for computing Lyapunov exponents

Beyn W-J, Lust A (2013)
Numerische Mathematik 123(2): 189-217.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Beyn, Wolf-JürgenUniBi; Lust, Alexander
Abstract / Bemerkung
In a previous paper (Beyn and Lust in Numer Math 113:357-375, 2009) we suggested a numerical method for computing all Lyapunov exponents of a dynamical system by spatial integration with respect to an ergodic measure. The method extended an earlier approach of Aston and Dellnitz (Comput Methods Appl Mech Eng 170:223-237, 1999) for the largest Lyapunov exponent by integrating the diagonal entries from the -decomposition of the Jacobian for an iterated map. In this paper we provide an asymptotic error analysis of the method for the case in which all Lyapunov exponents are simple. We employ Oseledec multiplicative ergodic theorem and impose certain hyperbolicity conditions on the invariant subspaces that belong to neighboring exponents. The resulting error expansion shows that one step of extrapolation is enough to obtain exponential decay of errors.
Erscheinungsjahr
2013
Zeitschriftentitel
Numerische Mathematik
Band
123
Ausgabe
2
Seite(n)
189-217
ISSN
0029-599X
Page URI
https://pub.uni-bielefeld.de/record/2560140

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Beyn W-J, Lust A. Error analysis of a hybrid method for computing Lyapunov exponents. Numerische Mathematik. 2013;123(2):189-217.
Beyn, W. - J., & Lust, A. (2013). Error analysis of a hybrid method for computing Lyapunov exponents. Numerische Mathematik, 123(2), 189-217. doi:10.1007/s00211-012-0486-4
Beyn, W. - J., and Lust, A. (2013). Error analysis of a hybrid method for computing Lyapunov exponents. Numerische Mathematik 123, 189-217.
Beyn, W.-J., & Lust, A., 2013. Error analysis of a hybrid method for computing Lyapunov exponents. Numerische Mathematik, 123(2), p 189-217.
W.-J. Beyn and A. Lust, “Error analysis of a hybrid method for computing Lyapunov exponents”, Numerische Mathematik, vol. 123, 2013, pp. 189-217.
Beyn, W.-J., Lust, A.: Error analysis of a hybrid method for computing Lyapunov exponents. Numerische Mathematik. 123, 189-217 (2013).
Beyn, Wolf-Jürgen, and Lust, Alexander. “Error analysis of a hybrid method for computing Lyapunov exponents”. Numerische Mathematik 123.2 (2013): 189-217.

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