Chiellini Hamiltonian Lienard differential systems
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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2019-05-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2019/71/abstr.html |
| _version_ | 1828334316301582336 |
|---|---|
| author | Jaume Gine Jaume Llibre Claudia Valls |
| author_facet | Jaume Gine Jaume Llibre Claudia Valls |
| author_sort | Jaume Gine |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T21:31:41Z |
| format | Article |
| id | doaj.art-7be6b027557648ad9461f7763f200dee |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-13T21:31:41Z |
| publishDate | 2019-05-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-7be6b027557648ad9461f7763f200dee2022-12-22T02:29:08ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912019-05-01201971,18Chiellini Hamiltonian Lienard differential systemsJaume Gine0Jaume Llibre1Claudia Valls2 Univ. de Lleida, Lleida, Catalonia, Spain Univ. Autonoma de Barcelona, Catalonia, Spain Instituto Superior Tecnico, Lisboa, Portugal 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.http://ejde.math.txstate.edu/Volumes/2019/71/abstr.htmlLienard systemcenter-focus problemfirst integrals |
| spellingShingle | Jaume Gine Jaume Llibre Claudia Valls Chiellini Hamiltonian Lienard differential systems Electronic Journal of Differential Equations Lienard system center-focus problem first integrals |
| title | Chiellini Hamiltonian Lienard differential systems |
| title_full | Chiellini Hamiltonian Lienard differential systems |
| title_fullStr | Chiellini Hamiltonian Lienard differential systems |
| title_full_unstemmed | Chiellini Hamiltonian Lienard differential systems |
| title_short | Chiellini Hamiltonian Lienard differential systems |
| title_sort | chiellini hamiltonian lienard differential systems |
| topic | Lienard system center-focus problem first integrals |
| url | http://ejde.math.txstate.edu/Volumes/2019/71/abstr.html |
| work_keys_str_mv | AT jaumegine chiellinihamiltonianlienarddifferentialsystems AT jaumellibre chiellinihamiltonianlienarddifferentialsystems AT claudiavalls chiellinihamiltonianlienarddifferentialsystems |