Polynomial and rational first integrals for planar quasi-homogeneous polynomial differential systems

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Issue date
2013-10
Author
Giné, Jaume
Grau Montaña, Maite
Llibre, Jaume
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Giné, Jaume; Grau Montaña, Maite; Llibre, Jaume; . (2013) . Polynomial and rational first integrals for planar quasi-homogeneous polynomial differential systems. Discrete and Continuous Dynamical Systems, 2013, vol. 33, num. 10, p. 4531-4547. https://doi.org/10.3934/dcds.2013.33.4531.
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Abstract
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 polynomial differential system can be transformed into a differential system of the form u˙=uf(v), v˙=g(v) with f(v) and g(v) polynomials, and vice versa.
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http://hdl.handle.net/10459.1/49444
DOI
https://doi.org/10.3934/dcds.2013.33.4531
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Discrete and Continuous Dynamical Systems, 2013, vol. 33, num. 10, p. 4531-4547
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