TY - JOUR

T1 - Inverse problems for invariant algebraic curves: Explicit computations

AU - Christopher, Colin

AU - Llibre, Jaume

AU - Pantazi, Chara

AU - Walcher, Sebastian

PY - 2009/4/1

Y1 - 2009/4/1

N2 - 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.

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.

U2 - https://doi.org/10.1017/S0308210507001175

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

M3 - Article

VL - 139

SP - 287

EP - 302

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

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

SN - 0308-2105

ER -