Ergodic theory is a branch of mathematics that studies statistical properties of
deterministic dynamical systems.
In this context, statistical properties means properties which are expressed through the behavior of time averages of various functions along trajectories of dynamical systems.
The notion of deterministic dynamical systems assumes that
the equations determining the dynamics do not contain
any random perturbations, noise, etc.
Thus, the statistics with which we are concerned are properties of the dynamics.
Ergodic theory, like probability theory, is based on general notions of measure theory.
Its initial development was motivated by problems of statistical physics.
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