一个直接解释逻辑斯蒂克3-周期映射分支的公式

A Trick Formula to Illustrate the Period Three Bifurcation Diagram of the Logistic Map

中文关键词:  正定不等式  周期3-分支  逻辑斯蒂克映射.

英文关键词:positive definite formula  period-3 bifurcation  logistic map.

中文摘要:

      本文给出了一个解释逻辑斯蒂克3-周期映射分支的公式.在此公式的基础上我们对逻辑斯蒂克3-周期映射的分支给出了一个新的非常简单的严格的直接证明.这一结果因此简化了以前有关文献中关于这一结果的证明,并对其中某些不严格之处做了补充.

英文摘要:

      In this paper we develop an algebraic formula in analyzing the bifurcation of the logistic map. Based on this formula, we give a new, short and rigorous proof for the period-3 bifurcation diagram of the logistic map. Therefore, we simplify the work in previous references and improve some insufficiently rigorous slight defects in them.