标题： 动力系统的熵灵活性 显示英文标题

标题： Entropy Flexibility of Dynamical Systems

摘要： 受Katok的中间熵性质[Inst. Hautes Études Sci. Publ. Math. 51 (1980), 137-173]的启发，我们引入并研究了离散时间和连续时间动力系统的熵灵活性的概念。通过使用再生系统技术，我们证明了在几个系统类中存在这一性质，其中任何中间熵值都可以在严格遍历子系统上实现。此外，我们证明了Katok猜想的熵灵活性类似结果：熵灵活性是三维流形上的向量场和曲面微分同胚的典型性质。 显示英文摘要

摘要： Inspired by Katok's intermediate entropy property [Inst. Hautes \'Etudes Sci. Publ. Math. 51 (1980), 137-173], we introduce and study the notion of entropy flexibility for discrete-time and continuous-time dynamical systems. By using renewal systems techniques, we show that this property is present in several classes of systems where any intermediate value of entropy can be attained on a strictly ergodic sub-system. In addition, we prove an entropy flexibility analogue of Katok's conjecture: Entropy flexibility is a typical property for vector fields on 3-manifolds and surface diffeomorphisms.