Flows and foliations subordinate to nonintegrable plane fields

1.对于不可积的平面场，熵总是为零（Zung 2011）。提出了一种新的熵的定义，它包含了可微性.引入了不可积平面场对初始条件敏感依赖（SDIC）的概念，并构造了SDIC的一个非平凡候选.给定一个切触流形M和一个具有非奇异流的环面T，在M上构造了一个切触形式，它定义了给定的切触结构，并允许T是相关Reeb流的不变集.

1. Usual entropy always vanishes for nonintegrable plane fields (Zung 2011). We proposed a new definition of entropy which is involved in differentiability.2. We introduced the concept of sensitive dependence on initial conditions (SDIC) for nonintegrable plane fields and constructed a nontrivial candidate for SDIC.3. Given a contact manifold M and a torus T with a nonsingular flow, we constructed a contact form on M which defines the given contact structure and admits T as an invariant set of the associated Reeb flow.