Measures of full dimension on self-affine sets
Antti Käenmäki (2004)
Acta Universitatis Carolinae. Mathematica et Physica
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Antti Käenmäki (2004)
Acta Universitatis Carolinae. Mathematica et Physica
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Zhen, Fang-Xiong (2006)
International Journal of Mathematics and Mathematical Sciences
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Kesseböhmer, Marc, Stratmann, Bernd O. (2008)
The New York Journal of Mathematics [electronic only]
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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...
Dennis Sullivan (1979)
Publications Mathématiques de l'IHÉS
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Manfred Denker, Gerhard Keller, Mariusz Urbański (1990)
Studia Mathematica
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Myjak, Józef (2005)
Abstract and Applied Analysis
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Barreira, Luis, Schmeling, Jörg (1997)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Manfred Denker, R. Mauldin, Z. Nitecki, Mariusz Urbański (1998)
Fundamenta Mathematicae
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We show that the set of conical points of a rational function of the Riemann sphere supports at most one conformal measure. We then study the problem of existence of such measures and their ergodic properties by constructing Markov partitions on increasing subsets of sets of conical points and by applying ideas of the thermodynamic formalism.
Hofbauer, F. (1995)
Acta Mathematica Universitatis Comenianae. New Series
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