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Títol:
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Integrability of planar polynomial differential systems through linear differential equations
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Autor/a:
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Giacomini, Héctor; Giné, Jaume; Grau Montaña, Maite
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Notes:
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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.
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. |
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Matèries:
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-Planar polynomial system
-First integral
-Invariant curves
-Darboux integrability
-Equacions diferencials |
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Drets:
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(c) Rocky Mountain Mathematics Consortium, 2006
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Tipus de document:
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article
submittedVersion |
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Publicat per:
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Rocky Mountain Mathematics Consortium
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