We investigate various estimators based on extreme value theory (EVT) for determining the local fractal dimension of chaotic dynamical systems. In the limit of an infinitely long time series of an ergodic system, the average of the local fractal dimension is the system’s global attractor dimension. The latter is an important quantity that relates to the number of effective degrees of freedom of the underlying dynamical system, and its estimation has been a central topic in the dynamical systems literature since the 1980s. In this work, we propose a framework that combines phase space recurrence analysis with EVT to estimate the local fractal dimension around a particular state of interest. While the EVT framework allows for the analysis of high-dimensional complex systems, such as the Earth’s climate, its effectiveness depends on robust statistical parameter estimation for the assumed extreme value distribution. In this study, we conduct a critical review of several EVT-based local fractal dimension estimators, analyzing and comparing their performance across a range of systems. Our results offer valuable insights for researchers employing the EVT-based estimates of the local fractal dimension, aiding in the selection of an appropriate estimator for their specific applications.
Skip Nav Destination
Research Article| July 19 2023
Statistical performance of local attractor dimension estimators in non-Axiom A dynamical systems
Flavio Pons ;
Flavio Pons a)
(Conceptualization, Formal analysis, Investigation, Methodology, Writing – original draft)
LSCE-IPSL, CEA Saclay l’Orme des Merisiers, CNRS UMR 8212 CEA-CNRS-UVSQ, Université Paris-Saclay, 91191 Gif-sur-Yvette,
Search for other works by this author on:
Gabriele Messori ;
Flavio Pons, Gabriele Messori, Davide Faranda; Statistical performance of local attractor dimension estimators in non-Axiom A dynamical systems. Chaos 1 July 2023; 33 (7): 073143. https://doi.org/10.1063/5.0152370
Download citation file:
Don't already have an account? Register
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Could not validate captcha. Please try again.