区间连续自映射的奇周期点列

ON SEQUENCE OF ODD PERIODIE POINTS OF CONTINUOUS SELF-MAP OF INTERVAL

设f∈C·（I），I为一区间，pp（f）＝N（2k0＋1），k0≥1，本文证明了，在I上至少存在一单调点列其中x0（i）分别以[2（k0＋1）＋1]为周期，i＝1，2…，进一步，我们证明了具有简单周期轨道的奇周期点列的存在性．利用本文的结果，不难推出Block及Hart的非常重要的简单期轨道存在性的结论．

Let f∈C°(I) and pp (f) =N(2k0+1) with k0≥1, In this paper, we obtain there exists at least a monotonic sequence of odd periodic points where x0(i) is a [2(k0+ 1)+ 1] periodic point for all i≥1. Moreover, there isn't any n - periodic point in x0(i), x0(i+1))with n ∈ { 1,, 3, 5, ...,2 (0+i) - 1 }for all i≥1. Furtherly, we also find a useful monotonic sequence of odd periodic point with simple orbit for all i≥1. By the result,the theorem B of Block and Hart is easy to show.