Connectivity properties of Julia sets of Weierstrass elliptic functions

DOI10.1016/j.topol.2004.08.018zbMath1074.37029OpenAlexW2082735186WikidataQ123298958 ScholiaQ123298958MaRDI QIDQ2566260

Lorelei Koss, Jane M. Hawkins

Publication date: 22 September 2005

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2004.08.018

zbMATH Keywords

Julia setsCantor setMeromorphic functionsComplex dynamics

Mathematics Subject Classification ID

Related Items (20)

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 Sets of Escaping Points and Escaping Parameters for Elliptic Functions ⋮ Hausdorff dimension of the set of elliptic functions with critical values approaching infinity ⋮ DYNAMICS AND BIFURCATIONS OF A FAMILY OF RATIONAL MAPS WITH PARABOLIC FIXED POINTS ⋮ 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 ⋮ The Hausdorff dimension of Julia sets of meromorphic functions in the Speiser class ⋮ Unnamed Item ⋮ Single and double toral band Fatou components in meromorphic dynamics

Cites Work

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• Rational iteration: complex analytic dynamical systems
• On Rational Maps with Two Critical Points
• Iterates of meromorphic functions: I
• Dynamics of meromorphic maps : maps with polynomial schwarzian derivative
• Iterates of meromorphic functions III: Preperiodic domains
• Iteration of a class of hyperbolic meromorphic functions
• Iteration of meromorphic functions
• HAUSDORFF DIMENSION AND HAUSDORFF MEASURES OF JULIA SETS OF ELLIPTIC FUNCTIONS
• Parametrized dynamics of the Weierstrass elliptic function

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