Distinguishing endpoint sets from Erdős space

DOI10.1017/S0305004122000032zbMath1506.37064arXiv2006.04783OpenAlexW4287760210MaRDI QIDQ5043355

David Sumner Lipham

Publication date: 21 October 2022

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.04783

zbMATH Keywords

Julia setescaping orbits

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Topological spaces of dimension (leq 1); curves, dendrites (54F50) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (1)

A dichotomy for spaces near dimension zero

Cites Work

• Escaping endpoints explode
• Dynamical properties of some classes of entire functions
• The dimension of the rational points in Hilbert space
• Erdos space and homeomorphism groups of manifolds
• The Geometry of Julia Sets
• Dynamics of exp (z)
• Area and Hausdorff Dimension of Julia Sets 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
• Non-escaping endpoints do not explode
• A note on the topology of escaping endpoints
• Topological dynamics of exponential maps on their escaping sets
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