论文标题
依赖时间依赖的哈密顿量的弱渐近的准二流解决方案，以观察到天体力学
Weakly asymptotically quasiperiodic solutions for time-dependent Hamiltonians with a view to celestial mechanics
论文作者
论文摘要
我们考虑了平面三体问题，该问题被一个模型的天体扰动，该天体是及时衰减的时间依赖性扰动。我们假设给出了天体的运动，并且没有非零的渐近速度。我们证明了绕的轨道的存在，这些轨道及时地融合到了与与平面三体问题的哈密顿量相关的Quasiperiodic解决方案``关闭''的动作。 证明依赖于一个摘要定理，该定理包含本工作中介绍的数学复杂性的很大一部分。该定理是灵活的，可以应用于许多其他物理现象。它认为哈密顿矢量场是两个组成部分的总和。第一个具有准碘溶液，随着时间的流逝，第二次衰减在多项式上很快。我们证明了绕的轨道的存在，这些轨道会及时收敛到与与未扰动系统相关的Quasiperiodic解决方案``close''的一些动作。 它概括了以前的工作，其中考虑了更强的多项式衰减，并证明了与未受扰动系统相关的准膜轨道及时收敛的溶液。 在本文中包含的抽象定理中，扰动时的衰变过于衰减会强烈改变无穷大的动态。这种严重的困难需要对证据进行深入修改。这种新策略依赖于NASH-MOSER隐式函数定理的应用（先前的结果已通过固定点定理证明）和引入弱解决方案（在这种情况下，轨道不会收敛到与未扰动系统相关的Quasiperiodic溶液）。
We consider the planar three-body problem perturbed by a celestial body modeled as a time-dependent perturbation that decays in time. We assume that the motion of the celestial body is given and is unbounded with a non-zero asymptotic velocity. We prove the existence of orbits converging in time to some motions that are ``close'' to the quasiperiodic solutions associated with the Hamiltonian of the planar three-body problem. The proof relies on an abstract theorem that contains a substantial portion of the mathematical complexities presented in this work. This theorem is flexible and can be applied to many other physical phenomena. It considers Hamiltonian vector fields that are the sum of two components. The first possesses quasiperiodic solutions, and the second decays polynomially fast as time tends to infinity. We prove the existence of orbits converging in time to some motions that are ``close'' to the quasiperiodic solutions associated with the unperturbed system. It generalizes a previous work where a stronger polynomial decay in time was considered, and solutions converging in time to the quasiperiodic orbits associated with the unperturbed system were proved. In the abstract theorem contained in the present paper, the too-weak decay in time of the perturbation strongly modifies the dynamic at infinity. This serious difficulty requires a deep modification of the proof. This new strategy relies on the application of a Nash-Moser implicit function theorem (the previous result was proved with the fixed point theorem) and the introduction of weak solutions (in this case, the orbits do not converge to the quasiperiodic solutions associated with the unperturbed system).
