Upper bounds on attractor dimensions for lattices of arbitrary size

Abstract : By using the link between extreme value theory and Poincaré recurrences, we compute the attractor dimension D - namely the effective number of degrees of freedom - of systems whose dynamics consist of n non-interacting particles with Gaussian underlying distributions. We also derive a theoretical expression for D in terms of finite size limits and test its validity and applicability with numerical experiments. We find that D in a non-interacting lattice is noticeably lower than the lattice size itself. We then estimate the attractor dimension of a collection of time-series issued from conceptual dynamical systems, finance and climate datasets. We find that spatial correlation within the particles reduce the attractor dimension. We also derive numerically the upper boundary for D of non-Gaussian systems, as their dimension can exceed the Gaussian theoretical limit.
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Submitted on : Tuesday, March 20, 2018 - 11:35:47 PM
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Flavio Maria Emanuele Pons, Gabriele Messori, M Carmen Alvarez-Castro, Davide Faranda. Upper bounds on attractor dimensions for lattices of arbitrary size. 2018. ⟨hal-01650250v2⟩

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