标题： 非可积哈密顿系统的近似不变量的构造 显示英文标题

标题： Construction of approximate invariants for non-integrable Hamiltonian systems

摘要： 我们提出一种方法来构造非可积哈密顿动力系统的高阶多项式近似不变量（AI），并将其应用于现代基于环形的粒子加速器。利用一种形式为方阵的一圈变换映射的特殊性质，AI可以逐阶迭代地构建。通过用仿真数据评估AI，我们观察到AI的波动实际上是混沌的度量。通过在加速器中使用控制旋钮来最小化波动，可以扩大长期运动的稳定区域。 显示英文摘要

摘要： We present a method to construct high-order polynomial approximate invariants (AI) for non-integrable Hamiltonian dynamical systems, and apply it to modern ring-based particle accelerators. Taking advantage of a special property of one-turn transformation maps in the form of a square matrix, AIs can be constructed order-by-order iteratively. Evaluating AI with simulation data, we observe that AI's fluctuation is actually a measure of chaos. Through minimizing the fluctuations with control knobs in accelerators, the stable region of long-term motions could be enlarged.