Michael Blank
Multiplicative cascade models and multifractality
(16K, LaTeX)

ABSTRACT.  We construct a (chaotic) deterministic variant of random multiplicative 
cascade models of turbulence. It preserves the hierarchical tree 
structure, thanks to the addition of infinitesimal noise or finite-state 
Markov approximations of chaotic maps. The zero-noise limit can be 
handled by Perron-Frobenius theory, just as the zero-diffusivity limit 
for the fast dynamo problem. We prove also the absence of phase 
transitions in conservative random multiplicative cascade models, 
corresponding to the non divergence of statistical moments.