Mathematical Sciences: Hamiltonian Dynamical Systems

主要研究概周期系统的全局性质，椭圆型受限三体问题的稳定性和周期解，以及Sternberg-Moser归一化定理的推广。此外，他将研究几乎周期性轨迹的混沌和稳定行为。这些研究的出发点将是三体问题拉格朗日平衡点的范式理论。大约在地球和月球之间有两个所谓的拉格朗日点。这些稳定的点被认为是物质积累的地方。研究者将寻找其他这样的点以及混沌轨迹。有关这些空间位置的信息应该证明对人类探索月球和行星是有价值的。

The principal investigator will study the global properties of almost periodic systems, stability and periodic solutions in the elliptic restricted three body problem, and generalizations of the Sternberg-Moser normalization theorem. Additionally he will investigate chaotic and stable behavior of almost periodic trajectories. The starting point for these studies will be normal form theory for the Lagrange equilibrium point of the three body problem. Roughly between the Earth and the Moon lies two so called Lagrange points. These are stable points where it is believed bits of matter have accumulated. The investigator will search for other such points as well as for chaotic trajectories. Information concerning these locations in space should prove valuable to human exploration of the Moon and planets.