  We study the sequence of attraction rates of iterates of a dominant
superattracting holomorphic fixed point germ f:(C^2,0)->(C^2,0). By using
valuative techniques similar to those developed by Favre-Jonsson, we show that
this sequence eventually satisfies an integral linear recursion relation,
which, up to replacing f by an iterate, can be taken to have order at most two.
In addition, when the germ f is finite, we show the existence of a
bimeromorphic model of (C^2,0) where f satisfies a weak local algebraic
stability condition.
