Exotic topology in complex dynamics

DOI10.1016/j.indag.2015.08.003zbMath1418.37076OpenAlexW1129286414MaRDI QIDQ344723

Robert L. Devaney

Publication date: 24 November 2016

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.indag.2015.08.003

zbMATH Keywords

Cantor bouquetJulia setcomplex dynamicsSierpinski curveindecomposable continuum

Mathematics Subject Classification ID

Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Fractals (28A80) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Cites Work

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• Singular perturbations of complex polynomials
• The Geometry of Julia Sets
• Topological characterization of the Sierpiński curve
• The escape trichotomy for singularly perturbed rational maps
• Dynamic classification of escape time Sierpiński curve Julia sets
• Dynamics of exp (z)
• Area and Hausdorff Dimension of Julia Sets of Entire Functions
• A finiteness theorem for a dynamical class of entire functions
• An explosion point for the set of endpoints of the Julia set of λ exp (z)
• Hausdorff dimension of the hairs without endpoints for λ exp z
• Geometry and Dynamics of Quadratic Rational Maps
• Indecomposable continua in exponential dynamics
• Julia sets converging to filled quadratic Julia sets
• Julia sets converging to the unit disk

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