The method of Puiseux series and invariant algebraic curves
Keyword(s):
An explicit expression for the cofactor related to an irreducible invariant algebraic curve of a polynomial dynamical system in the plane is derived. A sufficient condition for a polynomial dynamical system in the plane to have a finite number of irreducible invariant algebraic curves is obtained. All these results are applied to Liénard dynamical systems [Formula: see text], [Formula: see text] with [Formula: see text]. The general structure of their irreducible invariant algebraic curves and cofactors is found. It is shown that Liénard dynamical systems with [Formula: see text] can have at most two distinct irreducible invariant algebraic curves simultaneously and, consequently, are not integrable with a rational first integral.
2020 ◽
Vol 150
(6)
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pp. 3231-3251
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2009 ◽
Vol 139
(2)
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pp. 287-302
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2005 ◽
Vol 15
(03)
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pp. 1033-1044
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2021 ◽
2007 ◽
Vol 5
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pp. 195-200
1989 ◽
Vol 03
(15)
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pp. 1185-1188
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