journal article
oaidoi:10.1016/j.topol.2004.08.018

Connectivity properties of Julia sets of Weierstrass elliptic functions

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Publication date
1 July 2005
Publisher
Elsevier B.V.
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    Abstract

    AbstractWe discuss the connectivity properties of Julia sets of Weierstrass elliptic ℘ functions, accompanied by examples. We give sufficient conditions under which the Julia set is connected and show that triangular lattices satisfy this condition. We also give conditions under which the Fatou set of ℘ contains a toral band and provide an example of an order two elliptic function on a square lattice whose Julia set is a Cantor set

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