Invariant algebraic surfaces of polynomial vector fields in dimension three

DOI10.1007/s10884-021-10080-8arXiv1907.12536OpenAlexW3206424088WikidataQ115382977 ScholiaQ115382977MaRDI QIDQ6182568

Jaume Llibre, Sebastian Walcher, Chara Pantazi, Niclas Kruff

Publication date: 21 December 2023

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.12536

zbMATH Keywords

Darboux integrabilityPoincaré problemnonassociative algebrasJacobi multiplier

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) Invariant manifolds for ordinary differential equations (34C45)

Cites Work

• Unnamed Item
• Bounds for sectional genera of varieties invariant under Pfaff fields
• First integrals of local analytic differential systems
• On the Poincaré problem for foliations of general type
• Holomorphic foliations in \(CP(2)\) having an invariant algebraic curve
• Equations de Pfaff algébriques
• A theorem on non-associative algebras and its application to differential equations
• Finite dimensional algebras without nilpotents over algebraically closed fields
• Local theory of nonlinear analytic ordinary differential equations
• The Poincaré problem for hypersurfaces invariant by one-dimensional foliations
• Projections of polynomial vector fields and the Poincaré sphere
• On the Poincaré problem
• Bounding the degree of solutions to Pfaff equations
• The Castelnuovo-Mumford regularity of an integral variety of a vector field on projective space.
• Projective varieties invariant by one-dimensional foliations
• The Poincaré problem in the nondicritical case
• Some problems in the geometry of foliations for the 60th anniversary of IMPA
• Invariant ideals of local analytic and formal vector fields
• GSV-index for holomorphic Pfaff systems
• A class of polynomial planar vector fields with polynomial first integral
• A Poincaré type inequality for one-dimensional multiprojective foliations
• Inverse Jacobi multipliers
• Local Darboux first integrals of analytic differential systems
• On the geometry of Poincaré's problem for one-dimensional projective foliations
• Feuilletages holomorphes de codimension 1: une étude locale dans le cas dicritique
• Elementary First Integrals of Differential Equations
• Residue formulas for logarithmic foliations and applications
• On algebraic solutions of algebraic Pfaff equations
• Basic Algebraic Geometry 1
• On the density of algebraic foliations without algebraic invariant sets
• On the Poincaré inequality for one-dimensional foliations

This page was built for publication: Invariant algebraic surfaces of polynomial vector fields in dimension three