On Hausdorff dimension of Julia sets of hyperbolic rational semigroups

DOI10.2996/kmj/1138043831zbMath0917.58038OpenAlexW2074641402WikidataQ122516311 ScholiaQ122516311MaRDI QIDQ1267467

Hiroki Sumi

Publication date: 5 August 1999

Published in: Kodai Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/398fc33ee466e7dc8a17692fb46f44ae64a20e2e

zbMATH Keywords

expandingJulia setHausdorff dimensionrational semigroup

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Dynamical systems over complex numbers (37F99)

Related Items (12)

Interaction cohomology of forward or backward self-similar systems ⋮ Lee-Yang zeros of the antiferromagnetic Ising model ⋮ Structure of Julia sets of polynomial semigroups with bounded finite postcritical set ⋮ Transversality family of expanding rational semigroups ⋮ Holomorphic correspondences related to finitely generated rational semigroups ⋮ The space of 2-generator postcritically bounded polynomial semigroups and random complex dynamics ⋮ Real analyticity of Hausdorff dimension for expanding rational semigroups ⋮ Pointwise Hölder exponents of the complex analogues of the Takagi function in random complex dynamics ⋮ On Hausdorff dimension of Julia sets of hyperbolic rational semigroups ⋮ Dynamical properties and structure of Julia sets of postcritically bounded polynomial semigroups ⋮ Uniformly perfect sets, rational semigroups, Kleinian groups and IFS’s ⋮ Dynamics of infinitely generated nicely expanding rational semigroups and the inducing method

Cites Work

• Pointwise Hölder exponents of the complex analogues of the Takagi function in random complex dynamics
• The Julia sets of the random iteration of rational functions
• The limit set of a Fuchsian group
• On Hausdorff dimension of Julia sets of hyperbolic rational semigroups
• On dynamics of hyperbolic rational semigroups
• Julia sets of rational semigroups
• The Dynamics of Semigroups of Rational Functions I
• Complex Dynamics and Renormalization (AM-135)
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