Multifractal formalism for expanding rational semigroups and random complex dynamical systems

DOI10.1088/0951-7715/28/8/2913zbMath1352.37139arXiv1311.6241OpenAlexW2963584977MaRDI QIDQ3196546

Johannes Jaerisch, Hiroki Sumi

Publication date: 29 October 2015

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.6241

zbMATH Keywords

Julia setHausdorff dimensionmultifractal formalismrandom complex dynamicsrational semigroupscomplex dynamical systemsrandom iterations

Mathematics Subject Classification ID

Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems (37F15) Generation, random and stochastic difference and differential equations (37H10) Dynamical systems with hyperbolic orbits and sets (37D05)

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Spectral gap property for random dynamics on the real line and multifractal analysis of generalised Takagi functions ⋮ The space of 2-generator postcritically bounded polynomial semigroups and random complex dynamics ⋮ Multifractal formalism for generalised local dimension spectra of Gibbs measures on the real line ⋮ Pointwise Hölder exponents of the complex analogues of the Takagi function in random complex dynamics ⋮ Negativity of Lyapunov exponents and convergence of generic random polynomial dynamical systems and random relaxed Newton's methods ⋮ Non-i.i.d. random holomorphic dynamical systems and the probability of tending to infinity

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