Darboux integrating factors: Inverse problems

Colin Christopher; Jaume Llibre; Chara Pantazi; Sebastian Walcher

doi:https://doi.org/10.1016/j.jde.2010.10.013

Darboux integrating factors: Inverse problems

Colin Christopher, Jaume Llibre, Chara Pantazi, Sebastian Walcher

Department of Mathematics

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

5 Citations (Scopus)

Abstract

We discuss planar polynomial vector fields with prescribed Darboux integrating factors, in a nondegenerate affine geometric setting. We establish a reduction principle which transfers the problem to polynomial solutions of certain meromorphic linear systems, and show that the space of vector fields with a given integrating factor, modulo a subspace of explicitly known "standard" vector fields, has finite dimension. For several classes of examples we determine this space explicitly. © 2010 Elsevier Inc.

Original language	English
Pages (from-to)	1-25
Journal	Journal of Differential Equations
Volume	250
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2010.10.013
Publication status	Published - 1 Jan 2011

Keywords

Integrating factor
Invariant algebraic curve
Polynomial differential system

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https://doi.org/10.1016/j.jde.2010.10.013

https://ddd.uab.cat/record/150472

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AB - We discuss planar polynomial vector fields with prescribed Darboux integrating factors, in a nondegenerate affine geometric setting. We establish a reduction principle which transfers the problem to polynomial solutions of certain meromorphic linear systems, and show that the space of vector fields with a given integrating factor, modulo a subspace of explicitly known "standard" vector fields, has finite dimension. For several classes of examples we determine this space explicitly. © 2010 Elsevier Inc.

KW - Integrating factor

KW - Invariant algebraic curve

KW - Polynomial differential system

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