Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2007-06-29
Brazilian Journal of Physics 39, 364-370 (2009)
Physics
Condensed Matter
Statistical Mechanics
8 pages, 12 figures
Scientific paper
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. Amongst these features are the following: i) The set of preimages of the attractor and of the repellor are embedded (dense) into each other. ii) The preimage layout is obtained as the limiting form of the rank structure of the fractal boundaries between attractor and repellor positions for the family of supercycle attractors. iii) The joint set of preimages for each case form an infinite number of families of well-defined phase-space gaps in the attractor or in the repellor. iv) The gaps in each of these families can be ordered with decreasing width in accord to power laws and are seen to appear sequentially in the dynamics generated by uniform distributions of initial conditions. v) The power law with log-periodic modulation associated to the rate of approach of trajectories towards the attractor (and to the repellor) is explained in terms of the progression of gap formation. vi) The relationship between the law of rate of convergence to the attractor and the inexhaustible hierarchy feature of the preimage structure is elucidated.
Moyano Luis G.
Robledo Alberto
No associations
LandOfFree
Dynamics towards 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 Dynamics towards the Feigenbaum attractor, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamics towards the Feigenbaum attractor will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-681928