Invariant hyperplanes and Darboux integrability for \(d\)-dimensional polynomial differential systems

DOI10.1016/S0007-4497(00)01061-7zbMath0992.37016WikidataQ127359186 ScholiaQ127359186MaRDI QIDQ1841207

Jaume Llibre, Gerardo Rodriguez

Publication date: 21 June 2001

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

zbMATH Keywords

polynomial vector fieldDarboux theory of integrabilityinvariant hyperplanesregular polynomial systems

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) Symmetries, invariants of ordinary differential equations (34C14) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15)

Related Items

Invariant parallels, invariant meridians and limit cycles of polynomial vector fields on some 2-dimensional algebraic tori in \(\mathbb R^3\) ⋮ Local integrability and linearizability of a \((1:-1:-1)\) resonant quadratic system ⋮ Limit cycles, invariant meridians and parallels for polynomial vector fields on the torus ⋮ Integrability and linearizability of symmetric three-dimensional quadratic systems ⋮ Integrability and linearizability of three dimensional vector fields ⋮ Invariant sets of second order differential equations ⋮ Global dynamics of a family of 3-D Lotka–Volterra systems ⋮ Darboux integrability and reversible quadratic vector fields ⋮ Invariant circles for homogeneous polynomial vector fields on the 2-dimensional sphere ⋮ Liouvillian first integrals for the planar Lotka-Volterra system ⋮ Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces

Cites Work

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