Fractal Dimensions in Coupled Map Lattices
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 . 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 .
KeywordsFractal Dimension Lyapunov Exponent Minimal Resolution Empty Region Decimal Logarithm
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