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arXiv · 1311.6241

Multifractal formalism for expanding rational semigroups and random complex dynamical systems

Johannes Jaerisch·Hiroki Sumi
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Abstract

We consider the multifractal formalism for the dynamics of semigroups of rational maps on the Riemann sphere and random complex dynamical systems. We elaborate a multifractal analysis of level sets given by quotients of Birkhoff sums with respect to the skew product associated with a semigroup of rational maps. Applying these results, we perform a multifractal analysis of the H\"older regularity of limit state functions of random complex dynamical systems.

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Johannes Jaerisch, Hiroki Sumi. 2013-11-25. Multifractal formalism for expanding rational semigroups and random complex dynamical systems. https://arxiv.org/abs/1311.6241

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