弱混沌Hamilton系统的混沌与Arnold条纹
Chaotic and Arnold stripes in weakly chaotic Hamiltonian systems
摘要：
弱混沌哈密顿系统的动力学行为强烈依赖于初始条件，而对于系统的一般性行为却没有明确的认识。使用两个不同的哈密顿系统，即一个粒子在一个开放的矩形台球和四个粒子全球耦合的离散晶格，我们表明，在这些模型中，从可积运动到弱混沌的过渡出现通过混沌条纹的非线性参数的增加。条纹表示初始条件的区间，这些初始条件产生混沌轨迹，并且随着系统的非线性参数而增加。在台球的情况下，初始条件是喷射角。对于高维系统和小的非线性，混沌条纹是Arnold扩散发生的初始条件。
英文摘要：
The dynamics in weakly chaotic Hamiltonian systems strongly depends on initial conditions and little can be affirmed about generic behaviors. Using two distinct Hamiltonian systems, namely one particle in an open rectangular billiard and four particles globally coupled on a discrete lattice, we show that in these models the transition from integrable motion to weak chaos emerges via chaotic stripes as the nonlinear parameter is increased. The stripes represent intervals of initial conditions which generate chaotic trajectories and increase with the nonlinear parameter of the system. In the billiard case the initial conditions are the injection angles. For higher-dimensional systems and small nonlinearities the chaotic stripes are the initial condition inside which Arnold diffusion occurs.
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