关于区间上的Lorenz映射

本文引进了变换ζ．首先，用比文［４］简捷的方法证明了Ｌｏｒｅｎｚ映射的Ｓａｒｋｏｖｓｋｉ定理并更正了文［４］中的一个错误，还得到了扩张的Ｌｏｒｅｎｚ映射中周期点的存在性与其扩张常数之间的关系．其次，证明了Ｌｏｒｅｎｚ映射与其在变换ζ的像具有相等的捏制行列式．此外，给出了广义的Ｌｏｒｅｎｚ映射的周期点的存在性适合Ｓａｒｋｏｖｓｋｉ序关系的一个充分条件

On Lorenz Maps of the Interval

The transformation ζ is defined in this paper.It is proved first that the Sarkovskii's theorem for Lorenz maps by using a much more simpler method than that used in and an error in is corrected, also it is obtained that the general relation between the existence of periodic orbits in an expanding Lorenz map and its expanding constants. Secondly, it is proved that Lorenz map f and its image ζ (f) under ζ have equal kneading determinants.Moreover, a sufficient condition is obtained so that the existence of periodic points in a generalized Lorenz map satisfying the Sarkovskii's order.