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Liénard and Riccati differential equations related via Lie Algebras
| 1. | Departament de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69, 25001 Lleida, Spain, Spain |
| 2. | Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona |
| [1] |
Jaume Llibre, Claudia Valls. On the analytic integrability of the Liénard analytic differential systems. Discrete & Continuous Dynamical Systems - B, 2016, 21 (2) : 557-573. doi: 10.3934/dcdsb.2016.21.557 |
| [2] |
A. Ghose Choudhury, Partha Guha. Chiellini integrability condition, planar isochronous systems and Hamiltonian structures of Liénard equation. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2465-2478. doi: 10.3934/dcdsb.2017126 |
| [3] |
Fangfang Jiang, Junping Shi, Qing-guo Wang, Jitao Sun. On the existence and uniqueness of a limit cycle for a Liénard system with a discontinuity line. Communications on Pure & Applied Analysis, 2016, 15 (6) : 2509-2526. doi: 10.3934/cpaa.2016047 |
| [4] |
Jitsuro Sugie, Tadayuki Hara. Existence and non-existence of homoclinic trajectories of the Liénard system. Discrete & Continuous Dynamical Systems, 1996, 2 (2) : 237-254. doi: 10.3934/dcds.1996.2.237 |
| [5] |
Min Hu, Tao Li, Xingwu Chen. Bi-center problem and Hopf cyclicity of a Cubic Liénard system. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 401-414. doi: 10.3934/dcdsb.2019187 |
| [6] |
Mats Gyllenberg, Yan Ping. The generalized Liénard systems. Discrete & Continuous Dynamical Systems, 2002, 8 (4) : 1043-1057. doi: 10.3934/dcds.2002.8.1043 |
| [7] |
Na Li, Maoan Han, Valery G. Romanovski. Cyclicity of some Liénard Systems. Communications on Pure & Applied Analysis, 2015, 14 (6) : 2127-2150. doi: 10.3934/cpaa.2015.14.2127 |
| [8] |
Robert I. McLachlan, Ander Murua. The Lie algebra of classical mechanics. Journal of Computational Dynamics, 2019, 6 (2) : 345-360. doi: 10.3934/jcd.2019017 |
| [9] |
Richard H. Cushman, Jędrzej Śniatycki. On Lie algebra actions. Discrete & Continuous Dynamical Systems - S, 2020, 13 (4) : 1115-1129. doi: 10.3934/dcdss.2020066 |
| [10] |
Bin Liu. Quasiperiodic solutions of semilinear Liénard equations. Discrete & Continuous Dynamical Systems, 2005, 12 (1) : 137-160. doi: 10.3934/dcds.2005.12.137 |
| [11] |
Robert Roussarie. Putting a boundary to the space of Liénard equations. Discrete & Continuous Dynamical Systems, 2007, 17 (2) : 441-448. doi: 10.3934/dcds.2007.17.441 |
| [12] |
Franz W. Kamber and Peter W. Michor. Completing Lie algebra actions to Lie group actions. Electronic Research Announcements, 2004, 10: 1-10. |
| [13] |
Rui L. Fernandes, Yuxuan Zhang. Local and global integrability of Lie brackets. Journal of Geometric Mechanics, 2021, 13 (3) : 355-384. doi: 10.3934/jgm.2021024 |
| [14] |
Monika Eisenmann, Etienne Emmrich, Volker Mehrmann. Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data. Evolution Equations & Control Theory, 2019, 8 (2) : 315-342. doi: 10.3934/eect.2019017 |
| [15] |
Tomás Caraballo, David Cheban. Almost periodic and asymptotically almost periodic solutions of Liénard equations. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 703-717. doi: 10.3934/dcdsb.2011.16.703 |
| [16] |
Wenbin Liu, Zhaosheng Feng. Periodic solutions for $p$-Laplacian systems of Liénard-type. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1393-1400. doi: 10.3934/cpaa.2011.10.1393 |
| [17] |
Tiantian Ma, Zaihong Wang. Periodic solutions of Liénard equations with resonant isochronous potentials. Discrete & Continuous Dynamical Systems, 2013, 33 (4) : 1563-1581. doi: 10.3934/dcds.2013.33.1563 |
| [18] |
Oǧul Esen, Hasan Gümral. Geometry of plasma dynamics II: Lie algebra of Hamiltonian vector fields. Journal of Geometric Mechanics, 2012, 4 (3) : 239-269. doi: 10.3934/jgm.2012.4.239 |
| [19] |
Giovanni De Matteis, Gianni Manno. Lie algebra symmetry analysis of the Helfrich and Willmore surface shape equations. Communications on Pure & Applied Analysis, 2014, 13 (1) : 453-481. doi: 10.3934/cpaa.2014.13.453 |
| [20] |
Pengliang Xu, Xiaomin Tang. Graded post-Lie algebra structures and homogeneous Rota-Baxter operators on the Schrödinger-Virasoro algebra. Electronic Research Archive, 2021, 29 (4) : 2771-2789. doi: 10.3934/era.2021013 |
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