Lorenz映射系统中连续整数周期轨道的存在性

以符号动力学为基础,改进了Lorenz映射的允字条件.定义了单调1-基本字节和单调0-基本字节的概念,这些单调基本字节形成了周期序列的所有可能的基本字节,因此在满足允字条件下,给寻找周期轨道的算法带来了很大方便.证明了一般Lorenz映射系统存在连续整数周期轨道的充要条件是存在某条件下的2个互素周期,克服了Sarkovskii关于连续整数周期点对于函数连续性的限制,而所讨论的Lorenz映射也没有作每个单调支为线性的要求.给出了一些例子中连续整数周期轨道的符号序列的算法与表达形式,所提出的算法效率高,并可在作相应变化后推广到其他动力系统中.

Consturctive periodic orbits in Lorenz maps systems

Based on symbolic dynamics,the admissibility conditions are improved and thus the concepts of monotone basic 1-strings and 0-strings are defined.The basic strings generate all the possible basic strings of any periodic series thus the concepts improve the algorithm of finding periods under the admissibility conditions.It provides a satisfactory and necessary condition for existence of consecutive periodic orbits of Lorenz maps,that is,there exist two co-prime periods under some conditions,which overcomes the restriction of continuity of the functions in the Sarkovskii's theorem on consecutive periods,and the Lorenz maps are not restricted within piecewise linear ones.A corresponding algorithm and results of consecutive periods by symbolic series are given for some examples.The algorithm is of high efficiency and can be extended to other dynamic systems after some corresponding variation.