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Displaying similar documents to “Conformal measures for rational functions revisited”

Boundedness of sublinear operators on the homogeneous Herz spaces.

Guoen Hu (2003)

Publicacions Matemàtiques

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Some boundedness results are established for sublinear operators on the homogeneous Herz spaces. As applications, some new theorems about the boundedness on homogeneous Herz spaces for commutators of singular integral operators are obtained.

Quantization Dimension Function and Ergodic Measure with Bounded Distortion

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.

Multifractal analysis for Birkhoff averages on Lalley-Gatzouras repellers

Henry W. J. Reeve (2011)

Fundamenta Mathematicae

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We consider the multifractal analysis for Birkhoff averages of continuous potentials on a class of non-conformal repellers corresponding to the self-affine limit sets studied by Lalley and Gatzouras. A conditional variational principle is given for the Hausdorff dimension of the set of points for which the Birkhoff averages converge to a given value. This extends a result of Barral and Mensi to certain non-conformal maps with a measure dependent Lyapunov exponent.

Elementary examples of Loewner chains generated by densities

Alan Sola (2013)

Annales UMCS, Mathematica

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We study explicit examples of Loewner chains generated by absolutely continuous driving measures, and discuss how properties of driving measures are reflected in the shapes of the growing Loewner hulls.

Dimensions of the Julia sets of rational maps with the backward contraction property

Huaibin Li, Weixiao Shen (2008)

Fundamenta Mathematicae

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Consider a rational map f on the Riemann sphere of degree at least 2 which has no parabolic periodic points. Assuming that f has Rivera-Letelier's backward contraction property with an arbitrarily large constant, we show that the upper box dimension of the Julia set J(f) is equal to its hyperbolic dimension, by investigating the properties of conformal measures on the Julia set.