论文标题
不变的KAM Tori：从理论到应用到系外行驶系统
Invariant KAM tori: from theory to applications to exoplanetary systems
论文作者
论文摘要
我们认为构建不变的托里（Tori）的经典问题是利用合适的汉密尔顿正常形式。这种方法可以通过Lie系列方法转化为显式计算算法，这些算法特别适合于天体力学领域的应用。首先，详细描述了构建Kolmogorov正常形式的算法。然后，提供了较低椭圆形的tori的延伸。在两种情况下，我们都采用相同的形式主义和符号，以使后者更容易理解。最后，它们都是以一种组合方式使用的，以仔细近似于围绕HD 4732恒星绕的两个行星的外星系统的世俗动力学近似。
We consider the classical problem of the construction of invariant tori exploiting suitable Hamiltonian normal forms. This kind of approach can be translated by means of the Lie series method into explicit computational algorithms, which are particularly suitable for applications in the field of Celestial Mechanics. First, the algorithm constructing the Kolmogorov normal form is described in detail. Then, the extension to lower-dimensional elliptic tori is provided. We adopt the same formalism and notations in both cases, with the aim of making the latter easier to understand. Finally, they are both used in a combined way in order to approximate carefully the secular dynamics of the extrasolar system hosting two planets orbiting around the HD 4732 star.
