Abstract: |
I study the behaviour of the discrete dynamical system on the positive quadrant of the real plane given by (x,y)->(y,(y+y^{-1})/x). Its behaviour is extraordinary, because the trajectories of the system seem to lie on smooth curves, however, they are chaotic, but this fact can be perceived only at scales of the order 10^-60. Relation of this with tropical geometry will be discussed. Similar dynamical systems will also be mentioned. This subject was started from my discussions with M.Kontsevich. |