On natural invariant measures on generalised iterated function systems.
Käenmäki, Antti (2004)
Annales Academiae Scientiarum Fennicae. Mathematica
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Käenmäki, Antti (2004)
Annales Academiae Scientiarum Fennicae. Mathematica
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Mrinal Kanti Roychowdhury (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
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The quantization dimension function for the image measure of a shift-invariant ergodic measure with bounded distortion on a self-conformal set is determined, and its relationship to the temperature function of the thermodynamic formalism arising in multifractal analysis is established.
Manfred Denker, Gerhard Keller, Mariusz Urbański (1990)
Studia Mathematica
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Franz Hofbauer (2009)
Commentationes Mathematicae Universitatis Carolinae
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We extend the notions of Hausdorff and packing dimension introducing weights in their definition. These dimensions are computed for ergodic invariant probability measures of two-dimensional Lorenz transformations, which are transformations of the type occuring as first return maps to a certain cross section for the Lorenz differential equation. We give a formula of the dimensions of such measures in terms of entropy and Lyapunov exponents. This is done for two choices of the weights...
William Parry (1973)
Compositio Mathematica
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Kim, Jeong H. (1995)
International Journal of Mathematics and Mathematical Sciences
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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...