Mathematics
and Computer Science Speaker Series
California State University, Stanislaus
Date: Friday, December 3, 2010
Time: 4:00 - 5:00 p.m
Room: P-164
Speaker: John Rock
Title: Partition zeta functions of self-similar measures
Abstract: For an Iterated Function System (IFS) on the unit
interval weighted by a probability vector we define a multifractal
spectrum for the self-similar Borel measure uniquely determined by the
weighted IFS as the abscissae of convergence of its partition zeta
functions. Partition zeta functions are Dirichlet series
determined by the self-similar Borel measure and a naturally defined
sequence of partitions. These partition zeta functions are indexed by
coarse Holder regularity and we show that the corresponding abscissae
of convergence equal the Hausdorff dimension of corresponding
Besicovitch subsets of the support of the measure. In the case of the
binomial measure, for instance, the classical Hausdorff multifractal
spectrum is recovered.