论文标题
Lyapunov指数和周期性轨道附近
The Lyapunov exponents and the neighbourhood of periodic orbits
论文作者
论文摘要
我们表明，可以轻松从单片矩阵的特征值获得周期轨道的Lyapunov指数。事实证明，简单稳定的周期性轨道的Lyapunov指数都是零，简单的周期性轨道只有一个正lyapunov指数，双重不稳定的周期性轨道具有两个不同的lyapunov指数，而两个正面的lyapunov指数则是复杂的lyapunov指数。我们提供了一个数字示例，以实现现实银河电位的周期性轨道。此外，中心歧管定理使我们能够表明，稳定，不稳定和双重不稳定的周期轨道分别是其附近附近的家庭，正常，部分和完全混乱的轨道的母亲。
We show that the Lyapunov exponents of a periodic orbit can be easily obtained from the eigenvalues of the monodromy matrix. It turns out that the Lyapunov exponents of simply stable periodic orbits are all zero, simply unstable periodic orbits have only one positive Lyapunov exponent, doubly unstable periodic orbits have two different positive Lyapunov exponents and the two positive Lyapunov exponents of complex unstable periodic orbits are equal. We present a numerical example for periodic orbits in a realistic galactic potential. Moreover, the center manifold theorem allowed us to show that stable, simply unstable and doubly unstable periodic orbits are the mothers of families of, respectively, regular, partially and fully chaotic orbits in their neighbourhood.
