The dynamics of piecewise monotonic maps under small perturbations
Peter Raith (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Displaying similar documents to “Hausdorff dimension for piecewise monotonic maps”
The dynamics of piecewise monotonic maps under small perturbations
The recurrence dimension for piecewise monotonic maps of the interval
Franz Hofbauer (2005)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We investigate a weighted version of Hausdorff dimension introduced by V. Afraimovich, where the weights are determined by recurrence times. We do this for an ergodic invariant measure with positive entropy of a piecewise monotonic transformation on the interval , giving first a local result and proving then a formula for the dimension of the measure in terms of entropy and characteristic exponent. This is later used to give a relation between the dimension of a closed invariant subset...
Continuity of the Hausdorff dimension for invariant subsets of interval maps.
Raith, P. (1994)
Acta Mathematica Universitatis Comenianae. New Series
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A note on the construction of nonsingular Gibbs measures
Manfred Denker, Michiko Yuri (2000)
Colloquium Mathematicae
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We give a sufficient condition for the construction of Markov fibred systems using countable Markov partitions with locally bounded distortion.
On the uniqueness of equilibrium states for piecewise monotone mappings
Manfred Denker, Gerhard Keller, Mariusz Urbański (1990)
Studia Mathematica
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Metric diophantine approximation in Julia sets of expanding rational maps
Richard Hill, Sanju L. Velani (1997)
Publications Mathématiques de l'IHÉS
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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.
Lasota-Yorke maps with holes : conditionally invariant probability measures and invariant probability measures on the survivor set
Carlangelo Liverani, Véronique Maume-Deschamps (2003)
Annales de l'I.H.P. Probabilités et statistiques
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