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Normal forms for certain singularities of vectorfields

Floris Takens — 1973

Annales de l'institut Fourier

C normal forms are given for singularities of C vectorfields on R , which are not flat, and for C vectorfields X on R 2 with X ( 0 ) = 0 , the 1-jet of X in the origin is a pure rotation, and some higher order jet of X attracting or expanding.

General multifractal analysis of local entropies

Floris TakensEvgeny Verbitski — 2000

Fundamenta Mathematicae

We address the problem of the multifractal analysis of local entropies for arbitrary invariant measures. We obtain an upper estimate on the multifractal spectrum of local entropies, which is similar to the estimate for local dimensions. We show that in the case of Gibbs measures the above estimate becomes an exact equality. In this case the multifractal spectrum of local entropies is a smooth concave function. We discuss possible singularities in the multifractal spectrum and their relation to phase...

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