Title

Elliptic Functions with Disconnected Julia Sets

Document Type

Article

Publication Date

6-2016

Department

Mathematics

Language

English

Publication Title

International Journal of Bifurcation and Chaos

Abstract

In this paper, we investigate elliptic functions of the form , where is the Weierstrass elliptic function on a real rhombic lattice. We show that a typical function in this family has a superattracting fixed point at the origin and five other equivalence classes of critical points. We investigate conditions on the lattice which guarantee that has a double toral band, and we show that this family contains the first known examples of elliptic functions for which the Julia set is disconnected but not Cantor.

Comments

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DOI

10.1142/S0218127416500954

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