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Generalized Kolmogorov entropy in the dynamics of multifractal generation

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  • Zanette, Damián H.

Abstract

We point out that applying a maximization principle on a Tsallis-like generalized form of the Kolmogorov entropy for iterated function systems, naturally provides a canonical statistical frame for the description of the multifractal measures generated by such dynamical processes. Multifractal spectra can then be characterized by usual statistical parameters — in particular, the “temperature”. We show that in the limit of zero “temperature” the multifractal measure collapses to a homogeneous distribution over a fractal support. For finite “temperatures”, multifractal spectra are studied numerically in an illustrative example.

Suggested Citation

  • Zanette, Damián H., 1996. "Generalized Kolmogorov entropy in the dynamics of multifractal generation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 223(1), pages 87-98.
    • Handle: RePEc:eee:phsmap:v:223:y:1996:i:1:p:87-98
    DOI: 10.1016/0378-4371(95)00294-4
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