Multifractal dimensions for invariant subsets of piecewise monotonic interval maps
Volume 176 / 2003
Fundamenta Mathematicae 176 (2003), 209-232
MSC: 37E05, 37C45, 28A80, 37B40, 37A35, 28A78, 37D20.
DOI: 10.4064/fm176-3-2
Abstract
The multifractal generalizations of Hausdorff dimension and packing dimension are investigated for an invariant subset $A$ of a piecewise monotonic map on the interval. Formulae for the multifractal dimension of an ergodic invariant measure, the essential multifractal dimension of $A$, and the multifractal Hausdorff dimension of $A$ are derived.
