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• W2963033939 abstract "We consider the dynamics of semi-hyperbolic semigroups generated byfinitely many rational maps on the Riemann sphere. Assuming that the nice open set condition holdsit is proved that there exists a geometric measure on the Julia set with exponent$h$ equal to the Hausdorff dimension of the Julia set. Both $h$-dimensional Hausdorffand packing measures are finite and positive on the Julia set and are mutually equivalentwith Radon-Nikodym derivatives uniformly separated from zero and infinity. All three fractaldimensions, Hausdorff, packing and box counting are equal. It is also proved that forthe canonically associated skew-product map there exists a unique $h$-conformal measure.Furthermore, it is shown that this conformal measure admits a unique Borel probability absolutelycontinuous invariant (under the skew-product map) measure. In fact these two measures areequivalent, and the invariant measure is metrically exact, hence ergodic." @default.
• W2963033939 created "2019-07-30" @default.
• W2963033939 creator A5024503738 @default.
• W2963033939 creator A5087163683 @default.
• W2963033939 date "2011-01-01" @default.
• W2963033939 modified "2023-10-16" @default.
• W2963033939 title "Measures and dimensions of Julia sets of semi-hyperbolic rational semigroups" @default.
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• W2963033939 doi "https://doi.org/10.3934/dcds.2011.30.313" @default.
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