论文标题
准周期性汉密尔顿系统中不变托里的流程图参数化方法
Flow map parameterization methods for invariant tori in quasi-periodic Hamiltonian systems
论文作者
论文摘要
本文的目的是提出一种计算非自治的准周期性汉密尔顿系统中不变托里和捆绑的参数化的方法。我们将流程图参数化方法推广到准周期设置。为此，我们介绍了纤维各向同性托里的概念，并绘制了素描定义，并在光纤互合式变形及其矩图上进行了概念。这些结构对于在合适的环境中起作用并导致魔术取消的证据至关重要，以保证存在共同体方程的解决方案。我们将算法应用于椭圆形限制的三个身体问题，并计算非谐振的三维不变托里及其在L1点附近的不变捆。
The purpose of this paper is to present a method to compute parameterizations of invariant tori and bundles in non-autonomous quasi-periodic Hamiltonian systems. We generalize flow map parameterization methods to the quasi-periodic setting. To this end, we introduce the notion of fiberwise isotropic tori and sketch definitions and results on fiberwise symplectic deformations and their moment maps. These constructs are vital to work in a suitable setting and lead to the proofs of magic cancellations that guarantee the existence of solutions of cohomological equations. We apply our algorithms in the Elliptic Restricted Three Body Problem and compute non-resonant 3-dimensional invariant tori and their invariant bundles around the L1 point.
