Multifractal formalism for expanding rational semigroups and random complex dynamical systems

13 Jul 2015  ·  Jaerisch Johannes, Sumi Hiroki ·

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. read more

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Dynamical Systems Complex Variables