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arXiv · 2310.10382

Equilibrium measures on Julia sets of random quadratic polynomials

Krzysztof Lech·Anna Zdunik
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Abstract

We consider sequences of compositions of quadratic polynomials $f_{c_n} (z) = z^2 + c_n$. For such sequences one can naturally generalize the definitions of the Julia set and basin of infinity from the autonomous case. In this setting the Julia set depends on a sequence $\omega = (c_0, c_1, ...)$. We study the equilibrium (harmonic) measure on such Julia sets. In particular, we calculate the Hausdorff dimension of the equilibrium measure and study its dependence on the ''scale of randomness''.

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Krzysztof Lech, Anna Zdunik. 2023-10-16. Equilibrium measures on Julia sets of random quadratic polynomials. https://arxiv.org/abs/2310.10382

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