Discrete-time dynamical system

Summary

A discrete-time dynamical system is a dynamical system in which time advances in whole steps. It is given by a single map $f$ of a space to itself, and the state after $n$ steps is the iterate $f^n(x)$. Such systems arise from sampling a continuous motion at regular times, from population models with generations, and from numerical methods. Many basic phenomena of dynamics, such as chaos and period doubling, are already visible in maps of an interval.