Algebraic integrability of planar polynomial vector fields by extension to Hirzebruch surfaces

DOI10.1007/s12346-022-00655-1zbMath1504.32060arXiv2202.06134OpenAlexW4296397624MaRDI QIDQ2675105

Francisco Monserrat, Elvira Pérez-Callejo, Carlos Galindo Pastor

Publication date: 20 September 2022

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.06134

zbMATH Keywords

planar polynomial vector fieldsrational first integralsHirzebuch surfaces

Mathematics Subject Classification ID

Singularities of holomorphic vector fields and foliations (32S65) Complex vector fields, holomorphic foliations, (mathbb{C})-actions (32M25)

Related Items (1)

A new \((3+1)\)-dimensional Sakovich equation in nonlinear wave motion: Painlevé integrability, multiple solitons and soliton molecules

Uses Software

• RationalFirstintegrals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Polynomial and rational first integrals for planar homogeneous polynomial differential systems
• A new algorithm for finding rational first integrals of polynomial vector fields
• On the Poincaré problem for foliations of general type
• Holomorphic foliations in \(CP(2)\) having an invariant algebraic curve
• Relationships between limit cycles and algebraic invariant curves for quadratic systems
• Algebraic integrability of foliations of the plane
• Singularities of vector fields on the plane
• The Poincaré problem for hypersurfaces invariant by one-dimensional foliations
• Algebraic solutions for polynomial systems with emphasis in the quadratic case
• Foliations in algebraic surfaces having a rational first integral
• Darboux integrability and the inverse integrating factor.
• Bounds on leaves of one-dimensional foliations
• Configurations of limit cycles and planar polynomial vector fields.
• Sheaves associated to holomorphic first integrals.
• On the Poincaré problem
• Differential Galois theory and non-integrability of planar polynomial vector fields
• Projective varieties invariant by one-dimensional foliations
• The Poincaré problem in the nondicritical case
• On the Darboux integrability of polynomial differential systems
• Foliations with isolated singularities on Hirzebruch surfaces
• Complex algebraic foliations
• On the computation of Darboux first integrals of a class of planar polynomial vector fields
• A class of polynomial planar vector fields with polynomial first integral
• The Poincaré problem, algebraic integrability and dicritical divisors
• Darboux theory of integrability in the sparse case
• On the remarkable values of the rational first integrals of polynomial vector fields
• Qualitative theory of planar differential systems
• Polarity with respect ot a foliation and Cayley-Bacharach Theorems
• Efficient algorithms for computing rational first integrals and Darboux polynomials of planar polynomial vector fields
• Algebraic Particular Integrals, Integrability and the Problem of the Center
• Some examples for the Poincaré and Painlevé problems
• Invariant algebraic curves and conditions for a centre
• Proximity inequalities and bounds for the degree of invariant curves by foliations of ℙ_{ℂ}²
• Chapters on algebraic surfaces
• A SURVEY ON THE BLOW UP TECHNIQUE
• On the characterization of algebraically integrable plane foliations
• Effective algebraic integration in bounded genus
• On the Poincaré inequality for one-dimensional foliations
• Birational Geometry of Foliations
• Reduction of Singularities of the Differential Equation Ady = Bdx

This page was built for publication: Algebraic integrability of planar polynomial vector fields by extension to Hirzebruch surfaces