离散扰动NLS方程组的Smale马蹄与混沌(Ⅰ)——Poincaré映射

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

基金项目: 国家自然科学基金资助项目(10471046);广东省自然科学基金资助项目(04300099)

Smale Horseshoes and Chaos in Discretized Perturbed NLS Systems(Ⅰ)——Poincaré Map

Department of Applied Mathematics, Guangzhou University, Guangzhou 510405, P. R. China;

摘要: 利用n维Conley-Moser条件证明了一类离散扰动非线性Schrdinger方程(NLS)的Smale马蹄的存在性．由以上结果，我们得到离散扰动NLS方程组存在不变集Λ，其动力系统与四符号变换拓扑共轭．
- 同宿轨道 /
- Poincaré映射 /
- Smale马蹄 /
- Conley-Moser条件
Abstract: The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger (NLS) equations was established by using n-dimensional versions of the Conley-Moser conditions.As a result,the discretized perturbed NLS system is shown to possess an invariant set Lambda on which the dynamics is topologically conjugate to a shift on four symbols.
- homoclinic orbit /
- Poincaré map /
- Smale horseshoes /
- Conley-Moser condition

[1]	Moser J.Stable and random motions in dynamical systems[A]In:Annals of Mathematics Studies[C].Princeton:77 Princeton University Press,NJ,1973.
[2]	Wiggins S.Global Bifurcations and Chaos, Analytic Methods[M].New York:Springer-Verlag,1988.
[3]	Li Y,Wiggins S.Homoclinic orbits and chaos in discretized perturbed NLS systems: Part II, Symbolic dynamics[J].J Nonlinear Sci,1997,7(4)：315—370. doi: 10.1007/BF02678141
[4]	GUO Bo-ling,CHEN Han-lin.Persistent homodinic orbits for a perturbed cubic-quintic nonlinear Schrodinger equation[J].J Partial Diff Eqs,2002,15(2):6—36.
[5]	Li Y,Wiggins S.Homoclinic orbits and chaos in discretized perturbed NLS systems: Part I,Homoclinic orbits[J].J Nonlinear Sci,1997,7(3)：211—269.

点击查看大图