A characterization of the generalized Liénard polynomial differential systems having invariant algebraic curves
The generalized Liénard polynomial differential systems are the differential systems of the form x′ = y, y′ = − f(x)y − g(x), where f and g are polynomials. We characterize all the generalized Liénard polynomial differential systems having an invariant algebraic curve. We show that the first four hi...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2022 |
| Country: | España |
| Institution: | Universitat de Lleida (UdL) |
| Repository: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/84042 |
| Online Access: | https://doi.org/10.1016/j.chaos.2022.112075 http://hdl.handle.net/10459.1/84042 |
| Access Level: | Open access |
| Keyword: | Liénard polynomial differential systems Invariant algebraic curve First integrals |
| Summary: | The generalized Liénard polynomial differential systems are the differential systems of the form x′ = y, y′ = − f(x)y − g(x), where f and g are polynomials. We characterize all the generalized Liénard polynomial differential systems having an invariant algebraic curve. We show that the first four higher coefficients of the polynomial in the variable y, defining the invariant algebraic curve, determine completely the generalized Liénard polynomial differential system. This fact does not hold for arbitrary polynomial differential systems. |
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