Invariant curves and analytic integrability of a planar vector field
type: Item
instance of: scholarly article
title: Invariant curves and analytic integrability of a planar vector field
zbMATH Open document ID: 1412.34110
published in: Journal of Differential Equations
publication date: 2018-12-03T00:00:00Z
review text: The paper contains an excessive number of results, stated in 21 theorems, 5 propositions, 2 lemmas and 4 examples. The authors deal with planar vector fields \(\mathbf{F}=(P,Q)^\top\) which are analytic near the isolated singularity at the origin. The results in the paper concern such things as the existence of irreducible invariant curves, the analytic integrability (or non-integrability), the existence of algebraic inverse integrating factors, etc. Most of the results are related to the quasi-homogeneous case. The introductory part has very useful review of previous results on the topic.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C45
zbMATH DE Number: 6987663
zbMATH Keywords: analytic vector fields
zbMATH Keywords: invariant curves
zbMATH Keywords: integrability
zbMATH Keywords: inverse integrating factor
author: Antonio Algaba
author: Cristóbal García
author: M. Reyes
reviewed by: Iliya D. Iliev
MaRDI profile type: Publication
full work available at URL: j.jde.2018.07.074
OpenAlex ID: W2885628322
cites work: The integrability problem for a class of planar systems
cites work: The center problem for a family of systems of differential equations having a nilpotent singular point
cites work: Rational integrability of two-dimensional quasi-homogeneous polynomial differential systems
cites work: Integrability of two dimensional quasi-homogeneous polynomial differential systems
cites work: Nilpotent systems admitting an algebraic inverse integrating factor over \(\mathbb{C}((x,y))\)
cites work: Q4768040
cites work: Invariant varieties through singularities of holomorphic vector fields
cites work: Local analytic integrability for nilpotent centers
cites work: Darboux integrability and the inverse integrating factor.
cites work: Necessary conditions for the existence of invariant algebraic curves for planar polynomial systems
cites work: On non-integrability of general systems of differential equations
cites work: On the first integrals in the center problem
cites work: Existence of inverse integrating factors and Lie symmetries for degenerate planar centers
cites work: Integrability, partial integrability, and nonintegrability for systems of ordinary differential equations
cites work: Q5434578
cites work: Equations de Pfaff algébriques
cites work: Polynomial first integrals for quasi-homogeneous polynomial differential systems
cites work: Holonomie et intégrales premières
cites work: Q3035865
cites work: Elementary First Integrals of Differential Equations
cites work: Reduction of Singularities of the Differential Equation Ady = Bdx
cites work: Elementary first integrals and algebraic invariant curves of differential equations
cites work: On the Poincaré problem
DOI: 10.1016/J.JDE.2018.07.074
Recommended article: Invariant curves and integrability of planar \(\mathcal C^r\) differential systems
Recommended article: Invariant curves and topological invariants for real plane analytic vector fields
Recommended article: A note on analytic integrability of planar vector fields
Recommended article: Analytic invariant curves for a planar mapping
Recommended article: Integral invariants and limit sets of planar vector fields
Recommended article: Analytic integrability for some degenerate planar vector fields
Recommended article: Invariant algebraic curves and rational first integrals for planar polynomial vector fields
Recommended article: Q4455805
Recommended article: Planar analytic vector fields with generalized rational first integrals
Recommended article: Q4855630
description: scientific article; zbMATH DE number 6987663