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Please apologize: the Bratelli-Vershik graph in which I'm interested is not this one but this one: graph2

At level $n$ there are $n$ vertices, there is one edge from each of the first $n-1$ vertices to the vertex just above at level $n-1$, and from the last vertex there are: one edge to the first vertex at level $n-1$, one edge to the second vertex, $2$ edges to the third vertex, ..., $2^{n-2}$ edges to the $(n-1)$-st vertex.

I'd like to know whether this graph induces a known example of transformation ?

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I think you need to formulate your question more precisely. Are you interested in a homeomorphism of a Cantor set that can be represented by the Bratteli diagram? If yes, you will have to specify an order on edges of the diagram. Or you stay in the framework of ergodic theory? –  SIB Aug 21 '12 at 15:37
    
@SIB I stay in the framework of ergodic theory. I am interested in properties such as Bernoulli, discrete spectrum, finite rank... –  Stéphane Laurent Aug 21 '12 at 15:44
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