MathDB

Given

0< c< 1

, we define

f(x) = \begin{cases} \frac{x}{c} & x \in [0,c] \\ \frac{1-x}{1-c} & x \in [c, 1] \end{cases}

Let

f^{n}(x)=f(f(...f(x)))

. Show that for each positive integer

n

f^{n}

has a non-zero finite nunber of fixed points which aren't fixed points of

f^k

for

k< n

Problem Statement