Sharkovskii定理所保证的周期轨道的最小个数
The Minimal Number of Periodic Orbits of Periods Guaranteed in Sharkovskii's Theorem
摘要：
设f（x）是从紧实区间到自身的连续函数，其周期轨道的最小周期为m，其中m不是2的整数次幂。然后，根据Sharkovsky定理，对于每个正整数n，其中m \prec n在下面定义的Sharkovsky序中，f（x）的具有最小周期n的周期轨道数目的下界是1。我们能把这个下界从1提高到更大的数吗？在本文中，我们给出了一个完整的回答这个问题。
英文摘要：
Let f(x) be a continuous function from a compact real interval into itself with a periodic orbit of minimal period m, where m is not an integral power of 2. Then, by Sharkovsky's theorem, for every positive integer n with m \prec n in the Sharkovsky's ordering defined below, a lower bound on the number of periodic orbits of f(x) with minimal period n is 1. Could we improve this lower bound from 1 to some larger number? In this paper, we give a complete answer to this question.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
