On hausdorff measures and SBR measures for parabolic rational maps

Manfred Heinz Denker, S. Rohde

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1763-1769
Number of pages7
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume9
Issue number9
DOIs
StatePublished - Jan 1 1999

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Rational Maps
Hausdorff Measure
Julia set
Hausdorff Dimension

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Applied Mathematics

Cite this

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On hausdorff measures and SBR measures for parabolic rational maps. / Denker, Manfred Heinz; Rohde, S.

In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 9, No. 9, 01.01.1999, p. 1763-1769.

Research output: Contribution to journalArticle

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