Polynomial first integrals via the Poincaré series

Authors:
Jaume Giné
Affiliations:
Departament de Matemítica, Universitat de Lleida, Avda. Jaume II, 69, 25001 Lleida, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

Citing 3
Cited 0

Polynomial first integrals of systems in the plane with center type linear part

Nonlinear Analysis: Theory, Methods & Applications
Implementation of a new algorithm of computation of the Poincaré-Liapunov constants

Journal of Computational and Applied Mathematics
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)

Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)

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Abstract

In (Appl. Math. 28 (2001) 17) a method to compute the Poincare-Liapunov constants for an arbitrary analytic differential system which has a linear center at the origin in function of the coefficients of the system was given. This method also computes the coefficients of the Poincare series in function of the same coefficients. In this work we use this method to determine polynomial differential systems which have a polynomial first integral.