Parametrized dynamics of the Weierstrass elliptic function

DOI10.1090/S1088-4173-04-00103-1zbMath1076.30027OpenAlexW1628277156MaRDI QIDQ4827381

Lorelei Koss, Jane M. Hawkins

Publication date: 16 November 2004

Published in: Conformal Geometry and Dynamics of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1088-4173-04-00103-1

zbMATH Keywords

Julia setsparameter spacecomplex dynamicsmeromorphic functionsholomorphic families

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) Iteration theory, iterative and composite equations (39B12) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items

Connectivity of Julia sets for Weierstrass elliptic functions on square lattices, Herman rings of elliptic functions, Elliptic Functions with Disconnected Julia Sets, Elliptic functions with critical points eventually mapped onto infinity, LOCALLY SIERPINSKI JULIA SETS OF WEIERSTRASS ELLIPTIC ℘ FUNCTIONS, Cantor and connected Julia sets of the parameterized Dixon elliptic functions, Unnamed Item, Hausdorff dimension of the set of elliptic functions with critical values approaching infinity, A family of elliptic functions with Julia set the whole sphere, Elliptic functions with critical orbits approaching infinity, Cantor Julia sets in a family of even elliptic functions, Stability of Cantor Julia sets in the space of iterated elliptic functions, PARAMETERIZED DYNAMICS FOR THE WEIERSTRASS ELLIPTIC FUNCTION OVER SQUARE PERIOD LATTICES, A fundamental dichotomy for Julia sets of a family of elliptic functions, Proof of a folklore Julia set connectedness theorem and connections with elliptic functions, Connectivity properties of Julia sets of Weierstrass elliptic functions, On the formulas of meromorphic functions with periodic Herman rings, Unnamed Item, Single and double toral band Fatou components in meromorphic dynamics

Uses Software

• Mathematica

Cites Work

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