On the planar integrable differential systems
MetadataShow full item record
Under very general assumptions we prove that the planar differential systems having a first integral are essentially the linear differential systems u˙ = u, ˙v = v. Additionally such systems always have a Lie symmetry. We improve these results for polynomial differential systems defined in R2 or C2.
Is part ofZAMP. Journal of Applied Mathematics and Physics, 2011, vol. 62, núm. 4, p. 567-574
Showing items related by title, author, creator and subject.
Polynomial and rational first integrals for planar quasi-homogeneous polynomial differential systems Giné, Jaume; Grau Montaña, Maite; Llibre, Jaume (American Institute of Mathematical Sciences, 2013-10)In this paper we find necessary and sufficient conditions in order that a planar quasi-homogeneous polynomial differential system has a polynomial or a rational first integral. We also prove that any planar quasi-homogeneous ...
Giné, Jaume; Grau Montaña, Maite; Llibre, Jaume (Universitat Autònoma de Barcelona, 2014)In this paper we find necessary and suficient conditions in order that a planar homogeneous polynomial differential system has a polynomial or rational first integral. We apply these conditions to linear and quadratic ...
Giacomini, Héctor; Giné, Jaume; Grau Montaña, Maite (Rocky Mountain Mathematics Consortium, 2006)In this work we consider rational ordinary differential equations dy/dx = Q(x, y)/P(x, y), with Q(x, y) and P(x, y) coprime polynomials with real coefficients. We give a method to construct equations of this type for ...