Multifractality of the Feigenbaum attractor and fractional derivatives

Details Multifractality of the Feigenbaum attractor and fractional derivatives Multifractality of the Feigenbaum attractor and fractional derivatives

2003-09-26

arxiv.org/abs/nlin/0309068v2

J. Stat. Phys. vol.121 Nos.5/6 pp.671--695 (2005)

Nonlinear Sciences

Chaotic Dynamics

20 pages, 5 figures, J.Stat.Phys. in press

Scientific paper

10.1007/s10955-005-7011-4

It is shown that fractional derivatives of the (integrated) invariant measure of the Feigenbaum map at the onset of chaos have power-law tails in their cumulative distributions, whose exponents can be related to the spectrum of singularities $f(\alpha)$. This is a new way of characterizing multifractality in dynamical systems, so far applied only to multifractal random functions (Frisch and Matsumoto (J. Stat. Phys. 108:1181, 2002)). The relation between the thermodynamic approach (Vul, Sinai and Khanin (Russian Math. Surveys 39:1, 1984)) and that based on singularities of the invariant measures is also examined. The theory for fractional derivatives is developed from a heuristic point view and tested by very accurate simulations.

Affiliated with

Also associated with

No associations

Rating

Multifractality of the Feigenbaum attractor and fractional derivatives 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 Multifractality of the Feigenbaum attractor and fractional derivatives, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multifractality of the Feigenbaum attractor and fractional derivatives will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-651226