EGU2020-16406
https://doi.org/10.5194/egusphere-egu2020-16406
EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Extremes for high dimensional chaotic systems

Tobias Kuna1,2, Valerio Lucarini1,2, Davide Faranda3, Jerouen Wouters1,2, and Viviane Baladi4
Tobias Kuna et al.
  • 1Centre for Mathematis of Planet Earth, University of Reading, Reading, UK. (t.kuna@reading.ac.uk)
  • 2The School of Mathematical, Physical and Computational Sciences, University of Reading, Reading, UK
  • 3CNRS, University of Paris-Saclay, France
  • 4LPSM, Laboratoire de Probabilités, Statistique et Modélisation, Sorbonne Université, France

Extremes are related to high impact and serious hazard events and hence their study and prediction have been and continue to be highly relevant for all kind of applications in geoscience and beyond. Extreme value theory is promising to be able to predict them reliably and robustly. In the last fifteen years the classical extreme value theory for stochastic processes has been extended to dynamical systems and has been related to properties of physical measure (statistical properties of the system), return and hitting times. We will review what one can say for highly dimensional perfectly chaotic systems.  We will concentrate on relations between the index of the extreme distribution and invariants of the underlying dynamical system which are stable, in the sense that they will continuously depend on changing parameters in the dynamics.  Furthermore, we explore whether there exists a response theory for extremes, that is, whether the change of extremes can be quantitatilvely expressed  in terms of changing parameters. 

 

How to cite: Kuna, T., Lucarini, V., Faranda, D., Wouters, J., and Baladi, V.: Extremes for high dimensional chaotic systems, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-16406, https://doi.org/10.5194/egusphere-egu2020-16406, 2020

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