1. Stability of attractor local dimension estimates in non-Axiom A dynamical systems
- Author
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Pons, Flavio, Messori, Gabriele, Faranda, Davide, Laboratoire des Sciences du Climat et de l'Environnement [Gif-sur-Yvette] (LSCE), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Extrèmes : Statistiques, Impacts et Régionalisation (ESTIMR), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Uppsala Universitet [Uppsala], Stockton University (Stockton), London Mathematical Laboratory, European Project: 948309,CENAE - EXCELLENT SCIENCE - European Research Council (ERC), European Project: 101003469,XAIDA, and European Project: 956396,EDIPI
- Subjects
[STAT]Statistics [stat] ,statistical estimation ,[SDU.STU.CL]Sciences of the Universe [physics]/Earth Sciences/Climatology ,Extreme value theory ,[NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD] ,Hausdorff dimension ,[NLIN]Nonlinear Sciences [physics] ,local attractor dimension - Abstract
We study different extreme value theory (EVT)-based estimators for the local Hausdorff dimension (also known as local attractor dimension) of dynamical systems. The attractor dimension is an important quantity related 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 80s. The framework considered here combines the analysis of recurrences in phase space with EVT to estimate the local attractor dimension in the neighborhood of a state of interest. While the EVT framework enables the analysis of highdimensional complex systems, such as the Earth's climate, its applicability relies on robust statistical parameter estimation for the assumed extreme value distribution. In this study
- Published
- 2023