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Generalized Kolmogorov entropy in the dynamics of multifractal generation

✍ Scribed by Damián H. Zanette

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
627 KB
Volume
223
Category
Article
ISSN
0378-4371

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✦ Synopsis

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.

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