Periodic Points of the Tent Map

★ 7/10functions Counting Recursion sequences

Problem

A function $f$ has domain and range $[0, 1]$ . Define $f_1 = f$ and $f_n = f \circ f_{n-1}$ ; solutions of $f_n(x) = x$ are called $n$ -th order periodic points of $f$ .

For

f(x) = \begin{cases} 2x, & 0 \le x \le \tfrac12, \\ 2 - 2x, & \tfrac12 < x \le 1, \end{cases}

how many $n$ -th order periodic points does $f$ have?

Answer

Solution

Difficulty	7/10
Topics	functions, Counting, Recursion, sequences

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