Electron. J. Differential Equations, Vol. 2019 (2019), No. 71, pp. 1-8.

Chiellini Hamiltonian Lienard differential systems

Jaume Gine, Jaume Llibre, Claudia Valls

We characterize the centers of the Chiellini Hamiltonian Lienard second-order differential equations $x'=y$, $y'=-f(x) y -g(x)$ where $g(x)=f(x) (k - \alpha (1 +\alpha) \int f(x) dx )$ with $\alpha, k \in \mathbb{R}$. Moreover we study the phase portraits in the Poincare disk of these systems when $f(x)$ is linear.

Submitted January 26, 2019. Published May 17, 2019.
Math Subject Classifications: 34C05, 34A34, 34C14.
Key Words: Lienard system; center-focus problem; first integrals.

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Jaume Giné
Departament de Matemàtica
Inspires Research Centre
Universitat de Lleida
Avda. Jaume II, 69
25001 Lleida, Catalonia, Spain
email: gine@matematica.udl.cat
Jaume Llibre
Departament de Matemàtiques
Universitat Autònoma de Barcelona
08193 Bellaterra, Barcelona, Catalonia, Spain
email: jllibre@mat.uab.cat
  Claudia Valls
Departamento de Matemática
Instituto Superior Técnico
Av. Rovisco Pais 1049-001
Lisboa, Portugal
email: cvalls@math.ist.utl.pt

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