q-deformed statistical-mechanical structure in the dynamics of the Feigenbaum attractor

Details q-deformed statistical-mechanical structure in the dynamics of the Feigenbaum attractor q-deformed statistical-mechanical structure in the dynamics of the Feigenbaum attractor

2007-10-04

arxiv.org/abs/0710.1047v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2 figures

Scientific paper

We show that the two complementary parts of the dynamics associated to the Feigenbaum attractor, inside and towards the attractor, form together a q -deformed statistical-mechanical structure. A time-dependent partition function produced by summing distances between neighboring positions of the attractor leads to a q-entropy that measures the fraction of ensemble trajectories still away at a given time from the attractor (and the repellor). The values of the q-indexes are given by the attractor's universal constants, while the thermodynamic framework is closely related to that first developed for multifractals.

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