单模动力系统第三大n-周期的存在性和唯一性

The Third Largest n-Period,s Properties of Existance and Uniqueness of a Unimodel Dynamic System

讨论关于单模动力系统 ,迭代是动力系统中最简单的模型 ,这些一维模型呈现很好的数学结构。某函数是区间 [0 ,1]上具有连续自映射的单模凸函数F(x) ,且该系统还依赖于某一特征实参数λ∈[0 ,1]。利用逆序列函数hn-1(λ)的性质 ,证明了对于单模凸函数F(x)第三大n—周期的MSS序列P=RLn-4 R2 ,存在某一自然数n0 ,当自然数n不小于该自然数时 ,则在某一区间 (λRLn- 4 R,λRLn- 4 )中 ,一定存在与该MSS序列相对应的特征实参数λRLN - 4 R2 。

This paper discusses a unimodel dynamic system where F(x) is a continuous self-mapping's function of unimodel convex . Iteration is simplest model in it. The one dimension model shows the most important structures in mathematics. The system depends on a real characteristic parameter λ∈ .Using the property of converse sequence of functions h n-1(λ),we shows that there exists a natural number n 0 for the MSS sequence of the third largest n-period of F(x) ,such that a real characteristic parameter (λ RL n-4R,λ RL n-4) which corresponds to the MSS sequence and the value is unique if n≥n 0.