Attractor dimensions for lattices of arbitrary size

Flavio Maria Emanuele Pons (1) , Gabriele Messori (2) , M Carmen Alvarez-Castro (3) , Davide Faranda (3, 4)

1 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna
2 Bolin Centre for Climate Research
3 LSCE - Laboratoire des Sciences du Climat et de l'Environnement [Gif-sur-Yvette]
4 London Mathematical Laboratory

By using the link between extreme value theory and Poincaré recurrences, we compute the at-tractor dimension-namely the effective number of degrees of freedom-when the dynamics consist of n non-interacting particles with a stochastic behavior. We derive the theoretical expression in terms of finite size limits and test its validity and applicability with numerical experiments. We find that the effective number of degrees of freedom in a stochastic lattice is noticeably lower than the lattice size itself. We then estimate the attractor dimension of a collection of time-series issued from finance and climate, and find that they are below the theoretical stochastic limit.

Domaines: Matière Condensée [cond-mat]; Autre [cond-mat.other]

Flavio Maria Emanuele Pons, Gabriele Messori, M Carmen Alvarez-Castro, Davide Faranda. Attractor dimensions for lattices of arbitrary size. 2017. ⟨hal-01650250v1⟩