Nonlinear Processes in Geophysics
Nonlinear Processes in Geophysics
NPG
Articles | Volume 33, issue 1
Articles | Volume 33, issue 1
https://doi.org/10.5194/npg-33-51-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/npg-33-51-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
Articles | Volume 33, issue 1
Research article
 | 
11 Feb 2026
Research article |  | 11 Feb 2026

On transversality and the characterization of finite time hyperbolic subspaces in chaotic attractors

Terence J. O'Kane and Courtney R. Quinn

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This preprint is open for discussion and under review for Nonlinear Processes in Geophysics (NPG).
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Cited articles

Arbanel, H. D., Brown, R., and Kennel, M. B.: Variation of Lyapunov exponents on a strange attractor, J. Nonlin. Sci., 175–199, https://doi.org/10.1007/BF01209065, 1991. a
Axelsen, A. R., O'Kane, T. J., Quinn, C. R., and Bassom, A. P.: Hyperbolicity and Southern Hemisphere Persistent Synoptic Events, J. Adv. Model. Earth Syst., 17, e2024MS004834, https://doi.org/10.1029/2024MS004834, 2025. a, b, c, d, e, f, g
Ayers, D., Lau, J., Amezcua, J., Carrassi, A., and Ojha, V.: Supervised machine learning to estimate instabilitiesin chaotic systems: Estimation of local Lyapunov exponents, Q. J. Roy. Meteorol. Soc., 1236–1262, https://doi.org/10.1002/qj.4450, 2023.  a
Beims, M. W. and Gallas, J. A. C.: Alignment of Lyapunov Vectors: a quantitative criterion to predict catastrophes?, Sci. Rep., 6, 1–7, https://doi.org/10.1038/srep37102, 2016. a
Bochi, J. and Viana, M.: How frequently are dynamical systems hyperbolic?, Modern Dynam. Syst. Appl., A19, 271–297, 2004. a
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Mathematical concepts and measures from dynamical systems theory are applied to identify commonalities across a diverse set of chaotic attractors to better understand the relationship between predictability, directions and rates of expansion and contraction of instabilities over finite time forecast horizons, and dimensionality. The patterns that emerge have broad implications for understanding many dynamical features of geophysical flows.
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