Displaying similar documents to “The Box Dimension of Completely Invariant Subsets for Expanding Piecewise Monotonic Transformations.”

Semicontinuity of dimension and measure for locally scaling fractals

L. B. Jonker, J. J. P. Veerman (2002)

Fundamenta Mathematicae

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The basic question of this paper is: If you consider two iterated function systems close to each other in an appropriate topology, are the dimensions of their respective invariant sets close to each other? It is well known that the Hausdorff dimension (and Lebesgue measure) of the invariant set does not depend continuously on the iterated function system. Our main result is that (with a restriction on the "non-conformality" of the transformations) the Hausdorff dimension is a lower semicontinuous...

Multifractal dimensions for invariant subsets of piecewise monotonic interval maps

Franz Hofbauer, Peter Raith, Thomas Steinberger (2003)

Fundamenta Mathematicae

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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.