Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: A comparative numerical study

Froyland G, Hüls T, Morriss GP, Watson TM (2013)
Physica D Nonlinear Phenomena 247(1): 18-39.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Froyland, Gary; Hüls, ThorstenUniBi; Morriss, Gary P.; Watson, Thomas M.
Abstract / Bemerkung
Covariant Lyapunov vectors or Oseledets vectors are increasingly being used for a variety of model analyses in areas such as partial differential equations, nonautonomous differentiable dynamical systems, and random dynamical systems. These vectors identify spatially varying directions of specific asymptotic growth rates and obey equivariance principles. In recent years new computational methods for approximating Oseledets vectors have been developed, motivated by increasing model complexity and greater demands for accuracy. In this numerical study we introduce two new approaches based on singular value decomposition and exponential dichotomies and comparatively review and improve two recent popular approaches of Ginelli et al. (2007) [36] and Wolfe and Samelson (2007) [37]. We compare the performance of the four approaches via three case studies with very different dynamics in terms of symmetry, spectral separation, and dimension. We also investigate which methods perform well with limited data. (C) 2012 Elsevier B.V. All rights reserved.
Stichworte
Multiplicative Ergodic Theorem; Sacker-Sell spectrum; Covariant Lyapunov vectors; Oseledets vectors; Lyapunov exponents; Dichotomy projectors
Erscheinungsjahr
2013
Zeitschriftentitel
Physica D Nonlinear Phenomena
Band
247
Ausgabe
1
Seite(n)
18-39
ISSN
0167-2789
Page URI
https://pub.uni-bielefeld.de/record/2565287

Zitieren

Froyland G, Hüls T, Morriss GP, Watson TM. Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: A comparative numerical study. Physica D Nonlinear Phenomena. 2013;247(1):18-39.
Froyland, G., Hüls, T., Morriss, G. P., & Watson, T. M. (2013). Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: A comparative numerical study. Physica D Nonlinear Phenomena, 247(1), 18-39. https://doi.org/10.1016/j.physd.2012.12.005
Froyland, G., Hüls, T., Morriss, G. P., and Watson, T. M. (2013). Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: A comparative numerical study. Physica D Nonlinear Phenomena 247, 18-39.
Froyland, G., et al., 2013. Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: A comparative numerical study. Physica D Nonlinear Phenomena, 247(1), p 18-39.
G. Froyland, et al., “Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: A comparative numerical study”, Physica D Nonlinear Phenomena, vol. 247, 2013, pp. 18-39.
Froyland, G., Hüls, T., Morriss, G.P., Watson, T.M.: Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: A comparative numerical study. Physica D Nonlinear Phenomena. 247, 18-39 (2013).
Froyland, Gary, Hüls, Thorsten, Morriss, Gary P., and Watson, Thomas M. “Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: A comparative numerical study”. Physica D Nonlinear Phenomena 247.1 (2013): 18-39.

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