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

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

doi:10.1080/02781070290034511

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

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

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Abstract

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 language	English
Pages (from-to)	867-880
Number of pages	14
Journal	Complex variables
Volume	47
Issue number	10
DOIs	https://doi.org/10.1080/02781070290034511
Publication status	Published - 2002

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abstract = "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.",

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AU - Kamphof, F.H.

AU - Streng, M.

AU - Twilt, F.

PY - 2002

Y1 - 2002

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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.

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DO - 10.1080/02781070290034511

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VL - 47

SP - 867

EP - 880

JO - Complex variables

JF - Complex variables

IS - 10

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

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