RL^(n-2)C(n≥3)型单峰周期轨道的存在性

ON THE EXISTENCE OF UNIMODAL PERIODIC ORBITS WITH_3TYPE RL^(n-2)C(n≥3)

设I=[0,1],f∈C°(I,I).研究了f中PL^(n-2)C(n≥3)型单峰周期轨道的存在性。此外,运用单峰动力学的方法较为简单地证明了定理:设fλ(x)=min{2x,1-λ(2x-1)}(■x∈I,λI).则有,(ⅰ)当0≤λ<1/2时,fλ中只有不动点而没有其他周期点;(ⅱ)当λ=1/2时,fλ中只有不动点和2-周期点,而没有其他周期点;(ⅲ)当1/2<λ≤1时,fλ中有6-周期点。

Let I=[0,1], f∈C^0(I.I). The existence of unimodal periodicorbits of f is discussed in this paper. Moreover, the following theoremis proved easily in unimodal dynamics. Theorem, Let f_λ(x)=min{2x,1-λ(2x-1)}((?)x∈I,λ∈I), then (i) f_λ has only fixed points and no otherperiodic points for λ∈[0,1/2);(ii) f_λ has only fixed points and 2-peri-odic points and no other periodic points for λ=1/2; (iii)f_λ has 6-periodicpoints for λ∈(1/2,1].