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Ergodic Properties and Julia Sets of Weierstrass Elliptic Functions

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Abstract.

 We discuss properties of the Julia and Fatou sets of Weierstrass elliptic ℘ functions arising from real lattices. We give sufficient conditions for the Julia sets to be the whole sphere and for the maps to be ergodic, exact, and conservative. We also give examples for which the Julia set is not the whole sphere.

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Authors and Affiliations

  1. University of North Carolina, Chapel Hill, NC, USA, USA

    Jane Hawkins

  2. Dickinson College, Carlisle, PA, USA, USA

    Lorelei Koss

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  1. Jane Hawkins
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  2. Lorelei Koss
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Received September 4, 2001; in revised form March 26, 2002

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Hawkins, J., Koss, L. Ergodic Properties and Julia Sets of Weierstrass Elliptic Functions. Monatsh Math 137, 273–300 (2002). https://doi.org/10.1007/s00605-002-0504-1

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  • DOI: https://doi.org/10.1007/s00605-002-0504-1

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