FRACTAL DIMENSION OF SPATIALLY EXTENDED SYSTEMS

A TORCINI, A POLITI, G P PUCCIONI, G DALESSANDRO

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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.

Original languageEnglish
Pages (from-to)85-101
Number of pages17
JournalPhysica. D, Nonlinear Phenomena
Volume53
Issue number1
Publication statusPublished - Oct 1991

Keywords

  • STRANGE ATTRACTORS
  • EMBEDDING DIMENSION
  • COHERENT STRUCTURES
  • DYNAMICAL-SYSTEMS
  • CHAOS
  • INTERMITTENCY
  • INVARIANT
  • EXPONENTS
  • ALGORITHM

Cite this

TORCINI, A., POLITI, A., PUCCIONI, G. P., & DALESSANDRO, G. (1991). FRACTAL DIMENSION OF SPATIALLY EXTENDED SYSTEMS. Physica. D, Nonlinear Phenomena, 53(1), 85-101.