TOPOLOGICAL AND DYNAMICAL STUDY OF NON-INTEGRABLE DISTRIBUTIONS

本文从全局的角度研究了流形上的不可积切线分布。特别是，我们采用了熵的概念，并研究了它在测量这种分布的复杂性方面的意义。不可积分布的熵的概念是由Bis在2005年首次提出的。我们给出了一个不同于他的定义，并证明了四维流形上非仿射恩格尔分布的熵的消失。

In this research we investigated non-integrable tangent distributions on manifolds from the global viewpoint. In particular, we took up the notion of entropy and examined its significance in measuring the complexity of such distributions. The notion of entropy for non-integrable distributions was first introduced by Bis in 2005. We gave a somewhat different definition from his one, and proved the vanishing of the entropy for non-affine Engel distributions on 4-dimensional manifolds.