Invariant Algebraic Curves of Generalized Liénard Polynomial Differential Systems

The Riccati polynomial differential systems are differential systems of the form [Formula: see text], [Formula: see text], where [Formula: see text] and [Formula: see text] for [Formula: see text] are polynomial functions. We characterize all the Riccati polynomial differential systems having an invariant algebraic curve. We show that the coefficients of the first four highest degree terms of the polynomial in the variable [Formula: see text] defining the invariant algebraic curve determine completely the Riccati differential system. A similar result is obtained for any Abel polynomial differential system.

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Invariant Algebraic Curves of Generalized Liénard Polynomial Differential Systems

Abstract: In this study, we focus on invariant algebraic curves of generalized Liénard polynomial differential systems x′=y, y′=−fm(x)y−gn(x), where the degrees of the polynomials f and g are m and n, respectively, and we correct some results previously stated.

Cited by 4 publications

References 16 publications

A Class of New Solvable Nonlinear Isochronous Systems and Their Classical Dynamics

A Class of New Solvable Nonlinear Isochronous Systems and Their Classical Dynamics

The solution of the Poincaré problem on the rational first integral for the Liénard polynomial differential equations

Characterization of the Riccati and Abel Polynomial Differential Systems Having Invariant Algebraic Curves

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