A family of non-Darboux-integrable quadratic polynomial differential systems with algebraic solutions of arbitrarily high degree

DOI10.1016/S0893-9659(03)90004-8zbMath1051.34023OpenAlexW2038171598MaRDI QIDQ1431824

Maite Grau, Javier Chavarriga

Publication date: 11 June 2004

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0893-9659(03)90004-8

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (9)

AN ALGORITHM FOR FINDING INVARIANT ALGEBRAIC CURVES OF A GIVEN DEGREE FOR POLYNOMIAL PLANAR VECTOR FIELDS ⋮ A survey on the inverse integrating factor ⋮ On the Darboux integrability of polynomial differential systems ⋮ Number of limit cycles for planar systems with invariant algebraic curves ⋮ Bifurcation analysis and integrability in the segmented disc dynamo with mechanical friction ⋮ Planar vector fields with a given set of orbits ⋮ Integrability of planar polynomial differential systems through linear differential equations ⋮ Polynomial inverse integrating factors for quadratic differential systems ⋮ NON-ALGEBRAIC LIMIT CYCLES FOR PARAMETRIZED PLANAR POLYNOMIAL SYSTEMS

Cites Work

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• Equations de Pfaff algébriques
• The Poincaré problem in the nondicritical case
• A family of quadratic polynomial differential systems with invariant algebraic curves of arbitrarily high degree without rational first integrals
• About a conjecture on quadratic vector fields

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