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

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

2008-01-18

arxiv.org/abs/0801.2948v2

Phys. Rev. E 77, 036213 (2008)

Physics

Condensed Matter

Statistical Mechanics

16 pages, 24 figures. Final published version. Minor corrections and typos added

Scientific paper

10.1103/PhysRevE.77.036213

We demonstrate that the dynamics towards 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. As an essential component in our demonstration we expose, at a previously unknown level of detail, the features of the dynamics of trajectories that either evolve towards the Feigenbaum attractor or are captured by its matching repellor. The dynamical properties of the family of periodic superstable cycles in unimodal maps are seen to be key ingredients for the comprehension of the discrete scale invariance features present at the period-doubling transition to chaos. We make clear the dynamical origin of the anomalous thermodynamic framework existing at the Feigenbaum attractor.

Affiliated with

Also associated with

No associations

Rating

q-Deformed Statistical-Mechanical Property in the Dynamics of Trajectories en route to the Feigenbaum Attractor does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with q-Deformed Statistical-Mechanical Property in the Dynamics of Trajectories en route to the Feigenbaum Attractor, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and q-Deformed Statistical-Mechanical Property in the Dynamics of Trajectories en route to the Feigenbaum Attractor will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-691513