Hello,


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.



Applications of discrete-time dynamics
The most natural way in which discrete time dynamics appears in physical systems is stroboscopically. The stroboscopic description of a periodically driven Hamiltonian system leads to the standard map, which exhibits a chaotic phase space. These systems have been realized with [microwaves](http://arxiv.org/abs/1302.1289) and with [atomic matter waves](http://arxiv.org/abs/1301.1615). The discrete time, stroboscopic description of a periodically driven system is essential here, since these are all one-dimensional systems which would not exhibit chaos if the Hamiltonian would be time independent.


