On the polynomial integrability of the Hoyer systems

DOI10.1016/j.jmaa.2012.10.011zbMath1263.34005OpenAlexW2060219670MaRDI QIDQ1931568

Claudia Valls, Jaume Llibre

Publication date: 14 January 2013

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.10.011

zbMATH Keywords

polynomial first integralshomogeneous differential systemsHoyer systems

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items

Integrability and linearizability problems of three dimensional Lotka-Volterra equations of rank-2

Cites Work

• Generalized rational first integrals of analytic differential systems
• Studies of the Hoyer system.
• Polynomial first integrals of the Lotka-Volterra system
• A criterion for the nonexistence of an additional analytic integral in Hamiltonian systems with \(n\) degrees of freedom
• Rational integration of the Lotka-Volterra system
• On non-integrability of general systems of differential equations
• Local Darboux first integrals of analytic differential systems
• On the existence of polynomial first integrals of quadratic homogeneous systems of ordinary differential equations
• Polynomial first integrals for quasi-homogeneous polynomial differential systems
• A note on Kowalevski exponents and the non-existence of an additional analytic integral
• A word of caution concerning the Yoshida criterion on algebraic integrability and Kowalevski exponents
• Local first integrals for systems of differential equations
• Integrability, partial integrability, and nonintegrability for systems of ordinary differential equations
• Necessary condition for the existence of algebraic first integrals