Projections of multifractal measures

Günter Radons

Physica A: Statistical Mechanics and its Applications, 1992, vol. 191, issue 1, 532-535

Abstract: Typical projections of simple multifractal measures with generalized dimensions Dq onto subspaces of dimension D are considered. It is known that for D0>D almost all projections have Euclidean support. Here it is shown that if in addition the generalized dimension D∞ increases beyond D, a typical projection changes from a singular continuous distribution to an absolutely continuous measure with a square-integrable, or even differentiable density. We thus find a phase transition from a multifractal to an ordinary distribution with trivial singularity spectrum.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:191:y:1992:i:1:p:532-535

DOI: 10.1016/0378-4371(92)90577-D

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