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Inverse problems for invariant algebraic curves: explicit computations

  • Colin Christopher (a1), Jaume Llibre (a2), Chara Pantazi (a3) and Sebastian Walcher (a4)

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.

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