Multivariate Böttcher equation for polynomials with non-negative coefficients

摘要

We give conditions for the multivariate Böttcher equation $ beta(f (x)) = beta(x)^{lambda} $ to have a solution, in the case where $ f : mathbb{R}^d rightarrow mathbb{R}^d $ is a polynomial with non-negative coefficients. The solution is constructed from the limit of the functional iterates $ -lambda^{-n} log f^{n}(x) $ .