We use dual graphs and generating sequences of valuations to compute the Poincaré series of non-divisorial valuations on function fields of dimension two. The Poincaré series are shown to reflect data from the dual graphs and hence carry equivalent information. This extends Galindo’s earlier results on the Poincaré series of divisorial valuations and consequently offers an alternative classification of valuations via Poincaré series.

Poincaré series, dual graphs of valuations, valuation theory.