qdeformed statisticalmechanical structure in the dynamics of the Feigenbaum attractor
Abstract
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 statisticalmechanical structure. A timedependent partition function produced by summing distances between neighboring positions of the attractor leads to a qentropy that measures the fraction of ensemble trajectories still away at a given time from the attractor (and the repellor). The values of the qindexes are given by the attractor's universal constants, while the thermodynamic framework is closely related to that first developed for multifractals.
 Publication:

arXiv eprints
 Pub Date:
 October 2007
 arXiv:
 arXiv:0710.1047
 Bibcode:
 2007arXiv0710.1047R
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 4 pages, 2 figures