**Definition** A *First Order Autonomous Recurrence Relation* is a [[Recurrence Relation]] of the form $y_{k} = u(y_{k-1}), \quad k= 1,2,3,\dots$where $u:\mathbb{R} \to \mathbb{R}$ is a given [[Function]] together with the initial condition $y_{0}\in\mathbb{R}$. **Closed Formula** Note that (using [[Function Iteration]]), $y_{k} = u^{[k]}(y_{0})$. See **Properties** [[Stationary Point of First Order Autonomous Recurrence Relation]] & [[Condition for Stability of Stationary Point of First Order Autonomous Recurrence Relation]].