Here is a Bratelli-Vershik graph: alt text http://www.freeimagehosting.net/newuploads/64jrg.jpg

This graph should (I do not master this topic) define a Vershik adic transformation $T$ on its path space.

• What are the invariant measure(s) on the path space for which $T$ is ergodic ?

• Is $T$ (isomorphic to) a known example of transformation in ergodic theory ?