I am a graduate student in the field of discrete-time dynamics. I am wondering about applications of this field outside of mathematics. More precisely, I would like to know if there are "real life" situations where dynamical notions provide a significant insight, or even better, a power of prediction.
For example, is there a situation which is naturally modelized by discrete-time dynamics in which chaos is observed (I know about Lorenz attractor and meteorology in the continuous-time case) ? Or a situation in which estimations of the radius of an attractor is helpful (let's say outside of algorithms to find numerical roots), or structural stability, Lyapunov exponents, entropy, etc. play a concrete role ?
Sorry if this question is a bit too general.