TY - JOUR

T1 - The Qualitative Behaviour of Newton Flows for Weierstrass' ℘-functions

AU - Helminck, G.F.

AU - Kamphof, F.H.

AU - Streng, M.

AU - Twilt, F.

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

U2 - 10.1080/02781070290034511

DO - 10.1080/02781070290034511

M3 - Article

VL - 47

SP - 867

EP - 880

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

SN - 1747-6933

IS - 10

ER -