华沙圈上连续映射的某些动力性质

Some Dynamical Properties of Continuous Maps on the Warsaw Circle

本文研究华沙圈上定义的连续映射的动力性质．指出对于定义在华沙圈上的连续自映射而言，有与线段自映射相应的Ｓａｒｋｏｖｓｋｉｉ定理，周期点集的闭包与回归点集的闭包相等，中心为周期点集的闭包，中心的深度不大于４，以及拓扑熵为零的充要条件是它的周期点的周期都是２的方幂．

In the present paper we study the dynamical properties of continuous maps on the Warsaw circle and show that for such a map a theorem similar to the Sarkovskii Theorem for interval maps holds, the closure of the set of periodic points coincides with the closure of the set of recurrent points, the depth of the center is not greater than 4, and the topological entropy is zero if and only if the periods of periodic points are the powers of 2.