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Inverse problems for invariant algebraic curves: explicit computations

Published online by Cambridge University Press:  25 March 2009

Colin Christopher ,
Jaume Llibre ,
Chara Pantazi  and
Sebastian Walcher
Colin Christopher
Affiliation:
Department of Mathematics and Statistics, University of Plymouth, Plymouth PL2 3AJ, UK ([email protected])
Jaume Llibre
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain ([email protected])
Chara Pantazi
Affiliation:
Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, ETSEIB, Av. Diagonal 647, 08028 Barcelona, Spain ([email protected])
Sebastian Walcher
Affiliation:
Lehrstuhl A für Mathematik, RWTH Aachen, 52056 Aachen, Germany ([email protected])
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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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 2 , April 2009 , pp. 287 - 302
Copyright
Copyright © Royal Society of Edinburgh 2009

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