Fractal dimension of spatially extended systems

Year: 1991

Authors: Torcini A., Politi A., Puccioni G.P., D´Alessandro G.

Autors Affiliation: Istituto Nazionale di Ottica,and INFN sezione di Firenze Largo E. Fermi 6, 50125 Firenze, Italy;
Physics Department, University of Strathclyde, Glasgow UK

Abstract: Properties of the invariant measure are numerically investigated in 1D chains of diffusively coupled maps. The coarse-grained fractal dimension is carefully computed in various embedding spaces, observing an extremely slow convergence towards the asymptotic value. This is in contrast with previous simulations, where the analysis of an insufficient number of points led the authors to underestimate the increase of fractal dimension with increasing the dimension of the embedding space. Orthogonal decomposition is also performed confirming that the slow convergence is intrinsically related to local nonlinear properties of the invariant measure. Finally, the Kaplan-Yorke conjecture is tested for short chains, showing that, despite the noninvertibility of the dynamical system, a good agreement is found between Lyapunov dimension and information dimension.

Journal/Review: PHYSICA D-NONLINEAR PHENOMENA

Volume: 53 (1)      Pages from: 85  to: 101

KeyWords: Strange Attractors; Embedding Dimension; Coherent Structures; Dynamical-systems; Chaos; Intermittency; Invariant; Exponents; Algorithm
DOI: 10.1016/0167-2789(91)90166-7

Citations: 36
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