q-Deformed Statistical-Mechanical Property in the Dynamics of Trajectories en Route to the Feigenbaum Attractor

We demonstrate that the dynamics toward and within the Feigenbaum attractor combine to form a q-deformed statistical-mechanical construction. The rate at which ensemble trajectories converge to the attractor (and to the repellor) is described by a q entropy obtained from a partition function generated by summing distances between neighboring positions of the attractor. The values of the q indices involved are given by the unimodal map universal constants, while the thermodynamic structure is closely related to that formerly developed for multifractals...

q-Deformed Statistical-Mechanical Property in the Dynamics of Trajectories en Route to the Feigenbaum Attractor Articles