Geodesic
Multifractal dimensions for invariant subsets of piecewise monotonic interval maps
Franz Hofbauer1 ; Peter Raith1 ; Thomas Steinberger2
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

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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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