Generalized Kolmogorov entropy in the dynamics of multifractal generation

Damián H. Zanette

Physica A: Statistical Mechanics and its Applications, 1996, vol. 223, issue 1, 87-98

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.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:223:y:1996:i:1:p:87-98

DOI: 10.1016/0378-4371(95)00294-4

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