Dynamical system

Summary

A dynamical system is a space of states together with a rule that moves each state forward in time. Time can be discrete, as in the repeated application of one map, or continuous, as in the solutions of an autonomous differential equation. The rule must be consistent: waiting for time $s$ and then for time $t$ is the same as waiting for time $s + t$. Dynamical systems model planets, populations, chemical reactions and many other processes, and their study asks what happens in the long run.