Stability of attractor local dimension estimates in non-Axiom A dynamical systems

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