dc.contributor.author |
Giacomini, Héctor |
dc.contributor.author |
Giné, Jaume |
dc.contributor.author |
Grau Montaña, Maite |
dc.date |
2016-09-13T08:10:50Z |
dc.date |
2016-09-13T08:10:50Z |
dc.date |
2006 |
dc.identifier |
0035-7596 |
dc.identifier |
http://hdl.handle.net/10459.1/57788 |
dc.identifier |
https://doi.org/10.1216/rmjm/1181069462 |
dc.identifier.uri |
http://hdl.handle.net/10459.1/57788 |
dc.description |
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 which a
first integral can be expressed from two independent solutions
of a second-order homogeneous linear differential equation.
This first integral is, in general, given by a non Liouvillian
function.
We show that all the known families of quadratic systems
with an irreducible invariant algebraic curve of arbitrarily high
degree and without a rational first integral, can be constructed
by using this method. We also present a new example of this
kind of family.
We give an analogous method for constructing rational
equations but by means of a linear differential equation of
first order. |
dc.description |
The second and third authors are partially supported by a MCYT grant number BFM 2002-04236-C02-01. The second author is partially supported by DURSI of Government of Catalonia’s Acció Integrada ACI2002-24 and by the Distinció de la Generalitat de Catalunya per a la promoció de la recerca universitària. |
dc.language |
eng |
dc.publisher |
Rocky Mountain Mathematics Consortium |
dc.relation |
MICYT/PN2000-2003/ BFM2002-04236-C02-01 |
dc.relation |
Versió preprint del document publicat a https://doi.org/110.1216/rmjm/1181069462 |
dc.relation |
Rocky Mountain Journal of Mathematics, 2006, vol. 36, núm 2, p. 457-485 |
dc.relation |
http://arxiv.org/abs/arXiv:math/0506035 |
dc.rights |
(c) Rocky Mountain Mathematics Consortium, 2006 |
dc.rights |
info:eu-repo/semantics/openAccess |
dc.subject |
Planar polynomial system |
dc.subject |
First integral |
dc.subject |
Invariant curves |
dc.subject |
Darboux integrability |
dc.subject |
Equacions diferencials |
dc.title |
Integrability of planar polynomial differential systems through linear differential equations |
dc.type |
article |
dc.type |
submittedVersion |