Complex Dynamics of Some Hamiltonian Systems: Nonintegrability of Equations of Motion
The main purpose of this paper is to study the complexity of some Hamiltonian systems from the view of nonintegrability, including the planar Hamiltonian with Nelson potential, double-well potential, and the perturbed elliptic oscillators Hamiltonian. Some numerical analyses show that the dynamic be...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/9326947 |
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| _version_ | 1841524771452354560 |
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| author | Jingjia Qu |
| author_facet | Jingjia Qu |
| author_sort | Jingjia Qu |
| collection | DOAJ |
| description | The main purpose of this paper is to study the complexity of some Hamiltonian systems from the view of nonintegrability, including the planar Hamiltonian with Nelson potential, double-well potential, and the perturbed elliptic oscillators Hamiltonian. Some numerical analyses show that the dynamic behavior of these systems is very complex and in fact chaotic in a large range of their parameter. I prove that these Hamiltonian systems are nonintegrable in the sense of Liouville. My proof is based on the analysis of normal variational equations along some particular solutions and the investigation of their differential Galois group. |
| format | Article |
| id | doaj-art-2c87891adebb447b91991c4346f3dba9 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-2c87891adebb447b91991c4346f3dba92025-02-03T05:47:26ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/93269479326947Complex Dynamics of Some Hamiltonian Systems: Nonintegrability of Equations of MotionJingjia Qu0School of Mathematics, Jilin University, Changchun 130012, ChinaThe main purpose of this paper is to study the complexity of some Hamiltonian systems from the view of nonintegrability, including the planar Hamiltonian with Nelson potential, double-well potential, and the perturbed elliptic oscillators Hamiltonian. Some numerical analyses show that the dynamic behavior of these systems is very complex and in fact chaotic in a large range of their parameter. I prove that these Hamiltonian systems are nonintegrable in the sense of Liouville. My proof is based on the analysis of normal variational equations along some particular solutions and the investigation of their differential Galois group.http://dx.doi.org/10.1155/2019/9326947 |
| spellingShingle | Jingjia Qu Complex Dynamics of Some Hamiltonian Systems: Nonintegrability of Equations of Motion Advances in Mathematical Physics |
| title | Complex Dynamics of Some Hamiltonian Systems: Nonintegrability of Equations of Motion |
| title_full | Complex Dynamics of Some Hamiltonian Systems: Nonintegrability of Equations of Motion |
| title_fullStr | Complex Dynamics of Some Hamiltonian Systems: Nonintegrability of Equations of Motion |
| title_full_unstemmed | Complex Dynamics of Some Hamiltonian Systems: Nonintegrability of Equations of Motion |
| title_short | Complex Dynamics of Some Hamiltonian Systems: Nonintegrability of Equations of Motion |
| title_sort | complex dynamics of some hamiltonian systems nonintegrability of equations of motion |
| url | http://dx.doi.org/10.1155/2019/9326947 |
| work_keys_str_mv | AT jingjiaqu complexdynamicsofsomehamiltoniansystemsnonintegrabilityofequationsofmotion |