Geodesic
Multifractal dimensions for invariant subsets of piecewise monotonic interval maps
Franz Hofbauer 1   ; Peter Raith 1   ; Thomas Steinberger 2
1 Institut für Mathematik Universität Wien Strudlhofgasse 4 A-1090 Wien, Austria
2 Institut für Ökonometrie, Operations Research und Systemtheorie Technische Universität Wien Argentinierstraße 8 A-1040 Wien, Austria
Fundamenta Mathematicae, Tome 176 (2003) no. 3, pp. 209-232 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm176-3-2
Keywords: multifractal generalizations hausdorff dimension packing dimension investigated invariant subset piecewise monotonic map interval formulae multifractal dimension ergodic invariant measure essential multifractal dimension multifractal hausdorff dimension derived

Franz Hofbauer  1   ; Peter Raith  1   ; Thomas Steinberger  2

1 Institut für Mathematik Universität Wien Strudlhofgasse 4 A-1090 Wien, Austria
2 Institut für Ökonometrie, Operations Research und Systemtheorie Technische Universität Wien Argentinierstraße 8 A-1040 Wien, Austria 
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Franz Hofbauer; Peter Raith; Thomas Steinberger. Multifractal dimensions for invariant subsets
 of piecewise monotonic interval maps. Fundamenta Mathematicae, Tome 176 (2003) no. 3, pp. 209-232. doi: 10.4064/fm176-3-2

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