WIAS Preprint No. 300, (1996)

On the completeness of multifractal spectra


  • Schmeling, Jörg
    ORCID: 0000-0001-6956-9463

2010 Mathematics Subject Classification

  • 37C45 37D35 28A80 37B25


  • multifractal analysis, Gibbs measures, depending conformal prellers, Lyapunov exponents, thermodynamic formalism, symbolic dynamics




We study the behavior of multifractal spectra on the boundary of their domains of definition. In particular, we show that the dimension of the set of points having minimal (or maximal) pointwise dimension is not necessarily zero. However, this situation may be neglected in the sense of Baire category for Gibbs measures on expanding conformal repellers.

Appeared in

  • Ergodic Theory Dynam. Systems 19 (1999( no. 6, pp. 1595--1616.

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