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Polynomial Vector Fields with Given Partial and First Integrals
2016The solutions of the inverse problem in ordinary differential equations have a very high degree of arbitrariness because of the unknown functions involved. To reduce this arbitrariness we need additional conditions. In this chapter we are mainly interested in the planar polynomial differential systems which have a given set of invariant algebraic ...
Jaume Llibre, Rafael Ramírez
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Polynomial and Rational First Integrals for Non–Autonomous Polynomial Hamiltonian Systems
Dynamic Systems and Applications, 2020Azucena Caicedo +2 more
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First integrals and Darboux polynomials of homogeneous linear differential systems
1995This paper studies rational and Liouvillian first integrals of homogeneous linear differential systems Y′=AY over a differential field k. Following [26], our strategy to compute them is to compute the Darboux polynomials associated with the system.
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Existence theorems for polynomial first integrals
Proceedings of the 1991 international symposium on Symbolic and algebraic computation, 1991openaire +1 more source
An efficient method for computing Liouvillian first integrals of planar polynomial vector fields
Journal of Differential Equations, 2021Luiz Duarte, Luis antonio da Mota
exaly
A New Algorithm for Finding Rational First Integrals of Polynomial Vector Fields
Qualitative Theory of Dynamical Systems, 2010Antoni Ferragut, Hector Giacomini
exaly
Piecewise-Polynomial Quadratures for Cauchy Singular Integrals
SIAM Journal on Numerical Analysis, 1986Apostolos Gerasoulis
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On the computation of Darboux first integrals of a class of planar polynomial vector fields
Journal of Mathematical Analysis and Applications, 2019Antoni Ferragut, C Galindo
exaly