离散扰动NLS方程组的Smale马蹄与混沌(Ⅰ)——Poincaré映射

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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

1.
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

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