Let $f:X\to X$ be a function and $f^n$ its $n$ th iteration. A point $x$ is called a periodic point of period $n$ of $f$ if it is a fixed point of $f^n$ The least $n$ for which $x$ is a fixed point of $f^n$ is called prime period or least period.

If $f$ is a function mapping $\mathbb{R}$ to $\mathbb{R}$ or $\mathbb{C}$ to $\mathbb{C}$ then a periodic point $x$ of prime period $n$ is called hyperbolic if $|(f^n)'(x)|\neq 1$ attractive if $|(f^n)'(x)|<1$ and repelling if $|(f^n)'(x)|>1$