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 Growth of attraction rates for iterates of a superattracting germ in dimension two


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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.



Author: William Gignac; Matteo Ruggiero

Source: https://archive.org/







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