 95179 Michael Blank
 Multiplicative cascade models and multifractality
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Mar 31, 95

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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 finitestate
Markov approximations of chaotic maps. The zeronoise limit can be
handled by PerronFrobenius theory, just as the zerodiffusivity 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.
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