The Qualitative Behaviour of Newton Flows for Weierstrass' ℘-functions

G.F. Helminck, F.H. Kamphof, M. Streng, F. Twilt

    Research output: Contribution to journalArticleAcademicpeer-review


    We study the continuous, desingularized Newton method for Weierstrass' ℘-functions. This leads to a family of autonomous differential equations in the plane, which depends on two complex parameters ω 1 and ω 2. For the associated flows there are, up to conjugacy, precisely three possibilities. These are determined by the form of the parallelogram spanned by ω 1 and ω 2: square, rectangular but not square, and non-rectangular.
    Original languageEnglish
    Pages (from-to)867-880
    Number of pages14
    JournalComplex variables
    Issue number10
    Publication statusPublished - 2002

    Cite this