The topological dimension of radial Julia sets

DOI10.1007/s40315-022-00449-1zbMath1501.37046arXiv2002.00853OpenAlexW3003396590WikidataQ121602431 ScholiaQ121602431MaRDI QIDQ2671673

David Sumner Lipham

Publication date: 3 June 2022

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.00853

zbMATH Keywords

zero-dimensionalcomplex exponentialradial Julia setmeandering set

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Dimension theory in general topology (54F45) Combinatorics and topology in relation with holomorphic dynamical systems (37F20) Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets (37F46)

Cites Work

• Escaping endpoints explode
• Dynamical properties of some classes of entire functions
• The finer geometry and dynamics of the hyperbolic exponential family
• Hausdorff dimension and conformal dynamics. II: Geometrically finite rational maps
• Fatou’s web
• The Geometry of Julia Sets
• On semiconjugation of entire functions
• Non-escaping endpoints do not explode
• Fast escaping points of entire functions
• Topological dynamics of exponential maps on their escaping sets
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