ErgocityAn infinite geodesic {$g$} is considered ergodic if for any open neighborhood {$N$} of the surface, the time spent by {$g$} in {$N$} is asymptotically equal to the fraction of the surface area occupied by {$N$}. We understand, for example, that the paths of billiard balls on an {$r\times s$} rectangle, where {$\frac rs$} is irrational, are all ergodic. Geodesics on boxes are in general not ergodic. [We will have more discussion on this in the future. By "in general" we mean in the sense of Almost all Boxes.] |