Fractal Dimensions in Coupled Map Lattices

  • A. Politi
  • G. D’Alessandro
  • A. Torcini
Part of the NATO ASI Series book series (NSSB, volume 208)


The discovery of erratic behaviour in deterministic systems opened entirely new per­spectives in the comprehension of dynamical behaviour of nonlinear systems. The existence of broad-band spectra no longer necessarily requires a coupling with an external uncontrollable thermal bath. Chaos, providing an information flow from irrelevant to relevant digits, naturally transforms the indetermination on the initial condition into a seemingly stochastic behaviour in time domain [1]. New classes of indicators have been consequently introduced, which allow to distinguish between truly stochastic motion and low-dimensional chaotic behaviour: Lyapunov exponents, metric entropy and fractal dimensions are dynamical invariants which measure the degree of chaoticity [2].


Fractal Dimension Lyapunov Exponent Minimal Resolution Empty Region Decimal Logarithm 
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Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • A. Politi
    • 1
  • G. D’Alessandro
    • 1
  • A. Torcini
    • 1
  1. 1.Istituto Nazionale di OtticaFirenzeItaly

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