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Bifractality of the devil’s staircase appearing in the burgers equation with brownian initial velocity |
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| Authors: | E Aurell U Frisch A Noullez M Blank |
| Institution: | (1) Center for Parallel Computers, Royal Institute of Technology, S-100 44 Stockholm, Sweden;(2) Mathematics Department, Stockholm University, S-106 91 Stockholm, Sweden;(3) Observatoire de Nice, URA CNRS 1362, B.P. 4229, 06304 Nice Cedex 4, France;(4) Institute for Information Transmission Problems, 101477 Moscow, Russia |
| Abstract: | It is shown that the inverse Lagrangian map for the solution of the Burgers equation (in the inviscid limit) with Brownian initial velocity presents a bifractality (phase transition) similar to that of the Devil’s staircase for the standard triadic Cantor set. Both heuristic and rigorous derivations are given. It is explained why artifacts can easily mask this phenomenon in numerical simulations. |
| Keywords: | Burgers equation fractals |
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