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On the completeness of multifractal spectra

Published online by Cambridge University Press:  01 December 1999

JÖRG SCHMELING
JÖRG SCHMELING
Affiliation:
Freie Universität Berlin, FB Mathematik und Informatik, Arnimallee 2-6, D–14195 Berlin, Germany (e-mail: shmeling@math.fu-berlin.de)
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Abstract

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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.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 6 , December 1999, pp. 1595 - 1616
Copyright
1999 Cambridge University Press