Global Behaviour of Integrable Complex Systems

像天气和太阳系这样多种多样的复杂系统是由非线性方程建模的，这些方程有难以捉摸的、不稳定的解。在一个地方，系统状态的极小变化可能会导致遥远地方系统行为的巨大变化。这种极端的敏感性通常被认为是混沌的迹象，但它也出现在完全有序的、可积的系统中。我们的主要目标是解决描述这种难以捉摸的解决方案的全球行为的巨大挑战，特别是在系统依赖于许多变量的情况下。

Complex systems as diverse as the weather and the solar system are modelled by non-linear equations that have elusive, unstable solutions. An infinitesimally small change in the state of the system at one place can lead to a vast change in its behaviour far away. Such extreme sensitivity is often take to be a sign of chaos, but it also occurs in completely ordered, integrable systems. Our main aim is to tackle the immense challenge of describing the global behaviour of such elusive solutions, particularly when the systems depend on many variables.