BIFRACTALITY OF THE DEVILS STAIRCASE APPEARING IN THE BURGERS-EQUATION WITH BROWNIAN INITIAL VELOCITY

Authors
AURELL E FRISCH U NOULLEZ A BLANK M
Citation
E. Aurell et al., BIFRACTALITY OF THE DEVILS STAIRCASE APPEARING IN THE BURGERS-EQUATION WITH BROWNIAN INITIAL VELOCITY, Journal of statistical physics, 88(5-6), 1997, pp. 1151-1164
Citations number
5
Categorie Soggetti
Mathematical Method, Physical Science","Physycs, Mathematical
Journal title
Journal of statistical physics → ACNP
ISSN journal
00224715
Volume
88
Issue
5-6
Year of publication
1997
Pages
1151 - 1164
Database
ISI
SICI code
0022-4715(1997)88:5-6<1151:BOTDSA>2.0.ZU;2-8
Abstract
It is shown that the inverse Lagrangian map for the solution of the Bu rgers equation (in the inviscid limit) with Brownian initial velocity presents a bifractality (phase transition) similar to that of the Devi l's staircase for the standard triadic Canter set. Both heuristic and rigorous derivations are given. It is explained why artifacts can easi ly mask this phenomenon in numerical simulations.