Complex Dynamics of Some Hamiltonian Systems: Nonintegrability of Equations of Motion
Author
Source
Advances in Mathematical Physics
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-03-03
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Qu, Jingjia. 2019. Complex Dynamics of Some Hamiltonian Systems: Nonintegrability of Equations of Motion. Advances in Mathematical Physics،Vol. 2019, no. 2019, pp.1-10.
https://search.emarefa.net/detail/BIM-1119051
Modern Language Association (MLA)
Qu, Jingjia. Complex Dynamics of Some Hamiltonian Systems: Nonintegrability of Equations of Motion. Advances in Mathematical Physics No. 2019 (2019), pp.1-10.
https://search.emarefa.net/detail/BIM-1119051
American Medical Association (AMA)
Qu, Jingjia. Complex Dynamics of Some Hamiltonian Systems: Nonintegrability of Equations of Motion. Advances in Mathematical Physics. 2019. Vol. 2019, no. 2019, pp.1-10.
https://search.emarefa.net/detail/BIM-1119051
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1119051