论文标题
二维图中的渐近（统计）周期性
Asymptotic (statistical) periodicity in two-dimensional maps
论文作者
论文摘要
在本文中，我们为对应于二维图的Frobenius-Perron操作员的渐近周期性提供了新的条件。严格扩展系统的渐近周期性的结果，即，在高维动力学系统中，系统的所有特征值大于一个。我们的新定理使该系统申请具有小于一个的本征值。证明的关键思想是按线集成定义的有限变化的函数。最后，我们引入了一个新的二维动力系统，该系统表现出具有不同周期的渐近周期性，具体取决于参数值，并讨论将我们的定理应用于模型。
In this paper we give a new sufficient condition for asymptotic periodicity of Frobenius-Perron operator corresponding to two--dimensional maps. The result of the asymptotic periodicity for strictly expanding systems, that is, all eigenvalues of the system are greater than one, in a high-dimensional dynamical systems was already known. Our new theorem enables to apply for the system having an eigenvalue smaller than one. The key idea for the proof is a function of bounded variation defined by line integration. Finally, we introduce a new two-dimensional dynamical system exhibiting the asymptotic periodicity with different periods depending on parameter values, and discuss to apply our theorem to the model.
