Title

Elliptic Functions with Critical Orbits Approaching Infinity

Document Type

Article

Publication Date

5-21-2010

Department

Mathematics

Language

English

Publication Title

Journal of Difference Equations and Applications

Abstract

We construct examples of elliptic functions, viewed as iterated meromorphic functions from the complex plane to the sphere, with the property that there exist one or more critical points which approach the essential singularity at ∞ under iteration but are not prepoles. We obtain many nonequivalent elliptic functions satisfying this property, including examples with Julia set the whole sphere as well as examples with nonempty Fatou set. These are the first examples of this type known to exist and provide examples to illustrate unusual chaotic measure theoretic behaviour studied by the third author and others.

Comments

Published as:
Hawkins, Jane, Lorelei Koss, and Janina Kotus. "Elliptic Functions with Critical Orbits Approaching Infinity." Journal of Difference Equations and Applications, 16, no. 5-6 (2010): 613-30.

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DOI

10.1080/10236190903203895

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