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Non-integrability of some hamiltonians with rational potentials
1. | Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, C. Jordi Giron 1-3 08034, Barcelona, Spain, Spain |
[1] |
Primitivo B. Acosta-Humánez, J. Tomás Lázaro, Juan J. Morales-Ruiz, Chara Pantazi. On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 1767-1800. doi: 10.3934/dcds.2015.35.1767 |
[2] |
Jaume Llibre, Yuzhou Tian. Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree -4. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021228 |
[3] |
Roman Šimon Hilscher. On general Sturmian theory for abnormal linear Hamiltonian systems. Conference Publications, 2011, 2011 (Special) : 684-691. doi: 10.3934/proc.2011.2011.684 |
[4] |
Sergey Rashkovskiy. Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 563-583. doi: 10.3934/jgm.2020024 |
[5] |
Alicia Cordero, José Martínez Alfaro, Pura Vindel. Bott integrable Hamiltonian systems on $S^{2}\times S^{1}$. Discrete and Continuous Dynamical Systems, 2008, 22 (3) : 587-604. doi: 10.3934/dcds.2008.22.587 |
[6] |
Guillaume Duval, Andrzej J. Maciejewski. Integrability of Hamiltonian systems with homogeneous potentials of degrees $\pm 2$. An application of higher order variational equations. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4589-4615. doi: 10.3934/dcds.2014.34.4589 |
[7] |
Mitsuru Shibayama. Non-integrability criterion for homogeneous Hamiltonian systems via blowing-up technique of singularities. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3707-3719. doi: 10.3934/dcds.2015.35.3707 |
[8] |
A. Ghose Choudhury, Partha Guha. Chiellini integrability condition, planar isochronous systems and Hamiltonian structures of Liénard equation. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2465-2478. doi: 10.3934/dcdsb.2017126 |
[9] |
Kaizhi Wang, Lin Wang, Jun Yan. Aubry-Mather theory for contact Hamiltonian systems II. Discrete and Continuous Dynamical Systems, 2022, 42 (2) : 555-595. doi: 10.3934/dcds.2021128 |
[10] |
Sonja Hohloch, Silvia Sabatini, Daniele Sepe. From compact semi-toric systems to Hamiltonian $S^1$-spaces. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 247-281. doi: 10.3934/dcds.2015.35.247 |
[11] |
Božidar Jovanović, Vladimir Jovanović. Virtual billiards in pseudo–euclidean spaces: Discrete hamiltonian and contact integrability. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 5163-5190. doi: 10.3934/dcds.2017224 |
[12] |
Shaoyun Shi, Wenlei Li. Non-integrability of generalized Yang-Mills Hamiltonian system. Discrete and Continuous Dynamical Systems, 2013, 33 (4) : 1645-1655. doi: 10.3934/dcds.2013.33.1645 |
[13] |
L. Búa, T. Mestdag, M. Salgado. Symmetry reduction, integrability and reconstruction in $k$-symplectic field theory. Journal of Geometric Mechanics, 2015, 7 (4) : 395-429. doi: 10.3934/jgm.2015.7.395 |
[14] |
Jaume Llibre, Claudia Valls. On the analytic integrability of the Liénard analytic differential systems. Discrete and Continuous Dynamical Systems - B, 2016, 21 (2) : 557-573. doi: 10.3934/dcdsb.2016.21.557 |
[15] |
Larry M. Bates, Francesco Fassò, Nicola Sansonetto. The Hamilton-Jacobi equation, integrability, and nonholonomic systems. Journal of Geometric Mechanics, 2014, 6 (4) : 441-449. doi: 10.3934/jgm.2014.6.441 |
[16] |
Jaume Llibre, Claudia Valls. Analytic integrability of a class of planar polynomial differential systems. Discrete and Continuous Dynamical Systems - B, 2015, 20 (8) : 2657-2661. doi: 10.3934/dcdsb.2015.20.2657 |
[17] |
Antonio Algaba, Cristóbal García, Jaume Giné. Analytic integrability for some degenerate planar systems. Communications on Pure and Applied Analysis, 2013, 12 (6) : 2797-2809. doi: 10.3934/cpaa.2013.12.2797 |
[18] |
Dung Le. Higher integrability for gradients of solutions to degenerate parabolic systems. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 597-608. doi: 10.3934/dcds.2010.26.597 |
[19] |
Kenneth R. Meyer, Jesús F. Palacián, Patricia Yanguas. Normally stable hamiltonian systems. Discrete and Continuous Dynamical Systems, 2013, 33 (3) : 1201-1214. doi: 10.3934/dcds.2013.33.1201 |
[20] |
Antonio Giorgilli. Unstable equilibria of Hamiltonian systems. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 855-871. doi: 10.3934/dcds.2001.7.855 |
2020 Impact Factor: 1.327
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