Multifractality of the Feigenbaum attractor and fractional derivatives
| dc.creator | Frisch, U. | |
| dc.creator | Khanin, K. | |
| dc.creator | Matsumoto, T. | |
| dc.date | 2003-09-26 | |
| dc.date | 2004-04-10 | |
| dc.date.accessioned | 2026-07-07T06:24:35Z | |
| dc.date.available | 2026-07-07T06:24:35Z | |
| dc.description | 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 $f(α)$. 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. | |
| dc.description | 20 pages, 5 figures, J.Stat.Phys. in press | |
| dc.identifier | https://arxiv.org/abs/nlin/0309068 | |
| dc.identifier | http://arxiv.org/abs/nlin/0309068 | |
| dc.identifier | J. Stat. Phys. vol.121 Nos.5/6 pp.671--695 (2005) | |
| dc.identifier | doi:10.1007/s10955-005-7011-4 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/96594 | |
| dc.subject | Chaotic Dynamics | |
| dc.subject | Mathematical Physics | |
| dc.title | Multifractality of the Feigenbaum attractor and fractional derivatives | |
| dc.type | text |