Inverse problems for invariant algebraic curves: Explicit computations

Colin Christopher; Jaume Llibre; Chara Pantazi; Sebastian Walcher

doi:https://doi.org/10.1017/S0308210507001175

Inverse problems for invariant algebraic curves: Explicit computations

Colin Christopher, Jaume Llibre, Chara Pantazi, Sebastian Walcher

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

18 Citations (Scopus)

Abstract

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are non-degenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes. © 2009 Copyright Royal Society of Edinburgh.

Original language	English
Pages (from-to)	287-302
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	139
DOIs	https://doi.org/10.1017/S0308210507001175
Publication status	Published - 1 Apr 2009

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title = "Inverse problems for invariant algebraic curves: Explicit computations",

abstract = "Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are non-degenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes. {\textcopyright} 2009 Copyright Royal Society of Edinburgh.",

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AU - Walcher, Sebastian

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AB - Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are non-degenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes. © 2009 Copyright Royal Society of Edinburgh.

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DO - https://doi.org/10.1017/S0308210507001175

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JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

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