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

6 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

Access to Document

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

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

Cite this

@article{1c086946f724469b8aa4e58865af47c7,

title = "Darboux integrating factors: Inverse problems",

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. {\textcopyright} 2010 Elsevier Inc.",

keywords = "Integrating factor, Invariant algebraic curve, Polynomial differential system",

author = "Colin Christopher and Jaume Llibre and Chara Pantazi and Sebastian Walcher",

year = "2011",

month = jan,

day = "1",

doi = "https://doi.org/10.1016/j.jde.2010.10.013",

language = "English",

volume = "250",

pages = "1--25",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Darboux integrating factors: Inverse problems

AU - Christopher, Colin

AU - Llibre, Jaume

AU - Pantazi, Chara

AU - Walcher, Sebastian

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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.

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

U2 - https://doi.org/10.1016/j.jde.2010.10.013

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

M3 - Article

VL - 250

SP - 1

EP - 25

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 1

ER -

Darboux integrating factors: Inverse problems

Abstract

Keywords

Access to Document

Fingerprint

Cite this