Inverse problems for invariant algebraic curves

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 nondegenerate, we give an explicit expression for these vector fields. In the general setting we p...

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Bibliographic Details
Authors: Cristopher, Colin, Llibre, Jaume|||0000-0002-9511-5999, Pantazi, Chara|||0000-0002-4394-404X, Walcher, Sebastian
Format: article
Publication Date:2007
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:44082
Online Access:https://ddd.uab.cat/record/44082
Access Level:Open access
Keyword:Corbes algèbriques
Equacions diferencials
Description
Summary: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 nondegenerate, 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.