题目描述
Define an iterative map by
$$
x_{n+1} = T(x_n)
$$
where $x_n \in [0,1]$.
Then, we define the period of a point: A fixed point, or point of period one, of the system we defined is a point at which $x_{n+1} = T(x_n) = x_n$, for all $n$. A fixed point of period N is a point at which $x_{n+N} = T^{N}(x_n) = x_n$, for all $n$. Note that the period we are considering here refers to the minimum positive period.
Now, Consider the tent map defined by
$$
T(x)=\begin{cases}
2\cdot x & 0\le x < 0.5 \\
2\cdot (1-x) & 0.5\le x \le 1
\end{cases}
$$
Give you a number of $N$, Your task is to calculate number of points of period $N$.