On hausdorff measures and SBR measures for parabolic rational maps

M. Denker; S. Rohde

doi:10.1142/S0218127499001243

On hausdorff measures and SBR measures for parabolic rational maps

M. Denker, S. Rohde

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

If J is the Julia set of a parabolic rational map having Hausdorff dimension h < 1, we show that Sullivan's h-conformal measure on J is either absolutely continuous or orthogonal with respect to the Hausdorff measures defined by the function f(t) = t^h(log 1/t)^τ, according to whether τ > τ₀ or τ ≤ τ₀ for some explicitly computable τ₀ > 0.

Original language	English (US)
Pages (from-to)	1763-1769
Number of pages	7
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	9
Issue number	9
DOIs	https://doi.org/10.1142/S0218127499001243
State	Published - Sep 1999

All Science Journal Classification (ASJC) codes

Modeling and Simulation
Engineering (miscellaneous)
General
Applied Mathematics

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10.1142/S0218127499001243

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title = "On hausdorff measures and SBR measures for parabolic rational maps",

abstract = "If J is the Julia set of a parabolic rational map having Hausdorff dimension h < 1, we show that Sullivan's h-conformal measure on J is either absolutely continuous or orthogonal with respect to the Hausdorff measures defined by the function f(t) = th(log 1/t)τ, according to whether τ > τ0 or τ ≤ τ0 for some explicitly computable τ0 > 0.",

author = "M. Denker and S. Rohde",

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AB - If J is the Julia set of a parabolic rational map having Hausdorff dimension h < 1, we show that Sullivan's h-conformal measure on J is either absolutely continuous or orthogonal with respect to the Hausdorff measures defined by the function f(t) = th(log 1/t)τ, according to whether τ > τ0 or τ ≤ τ0 for some explicitly computable τ0 > 0.

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On hausdorff measures and SBR measures for parabolic rational maps

Abstract

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