A dynamical system with oscillating time average
Given a discrete dynamical system T, one can ask what the time average of the system will be, that is, what is the average position of T^n(x) for large n? Birkhoff’s ergodic theorem, one of the most important results in ergodic theory, says that for an ergodic system on a finite measure space, the time average will in the limit as n -> infinity be equal to the space average for almost all initial