Definition:Gauss Map

Definition
Let $\closedint 0 1$ denote the closed interval from $0$ to $1$.

The Gauss map $T : \closedint 0 1 \to \closedint 0 1$ is defined by:
 * $\ds \map T x := \begin{cases} \fractpart {\dfrac 1 x} & : x \in \hointl 0 1 \\ 0 & : x = 0\end{cases}$

where $\fractpart \cdot$ denotes the fractional part.

Also known as
It is also called continued fractional map.