link between stationary processes and dynamical systems

Jun 2010
hi to everybody,

Could someone explain me what is the exact difference between a stationary process in probability and a process arising from a dynamical system, say an observable computed along a discrete orbit?
Suppose the existence of an invariant measure for the dynamical system built with a map T... this measure is built "afterwords" while the probabilistic stationary process is defined from the "beginning"...
The difference is really unclear to me...