When you analyze an autonomous, first-order discrete-time dynamical system (a.k.a. iterative map) one of the first things you should do is to find its equilibrium points (also called fixed points or stead...When you analyze an autonomous, first-order discrete-time dynamical system (a.k.a. iterative map) one of the first things you should do is to find its equilibrium points (also called fixed points or steady states), i.e., states where the system can stay unchanged over time.
Dynamical systems theory is the very foundation of almost any kind of rule-based models of complex systems. It consider show systems change over time, not just static properties of observations.