Herman rings of elliptic functions

DOI10.1007/s40598-020-00167-3zbMath1490.37065OpenAlexW3106004823MaRDI QIDQ823799

Monica Moreno-Rocha

Publication date: 16 December 2021

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

Full work available at URL: https://doi.org/10.1007/s40598-020-00167-3

zbMATH Keywords

elliptic functionsHerman ringsquasiconformal surgery

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Elliptic functions and integrals (33E05) Quasiconformal mappings in the complex plane (30C62) Combinatorics and topology in relation with holomorphic dynamical systems (37F20) Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics (37F31)

Related Items (4)

Cantor and connected Julia sets of the parameterized Dixon elliptic functions ⋮ Unnamed Item ⋮ On the formulas of meromorphic functions with periodic Herman rings ⋮ Single and double toral band Fatou components in meromorphic dynamics

Cites Work

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• On the configuration of Herman rings of meromorphic functions
• Remarks on Herman rings of transcendental meromorphic functions
• Dynamics and Julia sets of iterated elliptic functions
• The quasi-additivity law in conformal geometry
• Connectivity properties of Julia sets of Weierstrass elliptic functions
• A fundamental dichotomy for Julia sets of a family of elliptic functions
• On the quasiconformal surgery of rational functions
• Iteration of meromorphic functions
• Existence of herman rings for meromorphic functions
• Parametrized dynamics of the Weierstrass elliptic function
• Quasiconformal Surgery in Holomorphic Dynamics

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