Abstract: By using the algebraic analytical method, discussed the mean values of 1-DLogistic map X_n+1=μ-X_n². At the first time we find that the mean values are continuous but non-differentiable in chaotic region, also discussed that by using the algebraic analytical method and the structure of the unstable periodic orbits to solve the higher degree algebraic equations.

Key words: Logistic map, algebraic analytical method, mean value, Lyapunov exponent

摘要： 应用代数分析法对一维Logistic映射x_n+1=μ-x²_n的平均值进行了讨论，首次发现了平均值在混沌区对参数的连续不可微性。讨论了当参数μ=2时不稳定周期轨道的构造以及代数分析法在求解高次代数方程中的应用。

关键词: Logistic映射, 代数分析法, 平均值, Lyapunov指数