> [!NOTE] Definition (Periodic Points) > Let $y_{k}=u(y_{k-1}), \quad \text{for all }k\geq 1$where $u:\mathbb{R}\to \mathbb{R}$ is a given function and $y_{0}=\bar{y}$, be a [[First Order Autonomous Recurrence Relation|first order autonomous recurrence relation]]. > > Let $n\in \mathbb{N}^{+}.$ An $n$-periodic point of the equation is a point $p\in \mathbb{R}$ such that $y_{0}=p \implies y_{n}=p$ and $y_{k}\neq p$ for $k=1,2,\dots,n-1.$ # Properties .... # Applications **Examples**: