Planar analytic vector fields with generalized rational first integrals

DOI10.1016/S0007-4497(01)01083-1zbMath1032.34029MaRDI QIDQ5939009

Weigu Li, Xiang Zhang, Jaume Llibre

Publication date: 2 September 2001

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

zbMATH Keywords

monodromynormal formfirst integral

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35)

Related Items (10)

Algebraic integrability of nilpotent planar vector fields ⋮ On a conjecture on the integrability of Liénard systems ⋮ A new algorithm for finding rational first integrals of polynomial vector fields ⋮ Analytic partial-integrability of a symmetric Hopf-zero degeneracy ⋮ Local behavior of planar analytic vector fields via integrability ⋮ Planar vector fields with a given set of orbits ⋮ Integrability and non-integrability of periodic non-autonomous Lyness recurrences ⋮ A family of quadratic polynomial differential systems with invariant algebraic curves of arbitrarily high degree without rational first integrals ⋮ The geometrical demonstration of the order of resonant saddle points in \(\mathbb{C}^2\) ⋮ Polynomial first integrals via the Poincaré series

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