Periodic Solutions for the Generalized Anisotropic Lennard-Jones Hamiltonian
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- 作者：Jaume Llibre ; Yiming Long
- 关键词：Lennard ; Jones potential ; Circular periodic solutions ; Anisotropic Lennard ; Jones potential ; 70F10 ; 70H05 ; 34C23
- 刊名：Qualitative Theory of Dynamical Systems
- 出版年：2015
- 出版时间：October 2015
- 年：2015
- 卷：14
- 期：2
- 页码：291-311
- 全文大小：583 KB
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Yiming Long (2)
1. Departament de Matem脿tiques, Universitat Aut貌noma de Barcelona, Bellaterra, 08193, Barcelona, Catalonia, Spain
2. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, China - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics
Dynamical Systems and Ergodic Theory
Difference and Functional Equations - 出版者：Birkh盲user Basel
- ISSN：1662-3592
文摘
We characterize the circular periodic solutions of the generalized Lennard-Jones Hamiltonian system with two particles in \(\mathbb {R}^n\), and we analyze what of these periodic solutions can be continued to periodic solutions of the anisotropic generalized Lennard-Jones Hamiltonian system. We also characterize the periods of antiperiodic solutions of the generalized Lennard-Jones Hamiltonian system on \(\mathbb {R}^{2n}\), and prove the existences of \(0<\tau ^{*}\le \tau ^{**}\) such that this system possesses no \(\tau /2\)-antiperiodic solution for all \(\tau \in (0,\tau ^{*})\), at least one \(\tau /2\)-antiperiodic solution when \(\tau =\tau ^{*}\), precisely \(2^n\) families of \(\tau /2\)-antiperiodic circular solutions when \(\tau =\tau ^{**}\), and precisely \(2^{n+1}\) families of \(\tau /2\)-antiperiodic circular solutions when \(\tau >\tau ^{**}\). Each of these circular solution families is of dimension \(n-1\) module the \(S^1\)-action. Keywords Lennard-Jones potential Circular periodic solutions Anisotropic Lennard-Jones potential