On measures resisting multifractal analysis
classification
🧮 math.DS
keywords
invariantmeasuremeasuresmultifractalanalysiscirclecompactconstruct
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Any ergodic measure of a smooth map on a compact manifold has a multifractal spectrum with one point - the dimension of the measure itself - at the diagonal. We will construct examples where this fails in the most drastic way for invariant measures invariant under linear maps of the circle.
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