Summary.
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 \( -\lambda^{-n} \log f^{n}(x) \).
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Received: April 6, 1999, revised version: July 5, 2000.
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Jones, O. Multivariate Böttcher equation for polynomials with non-negative coefficients. Aequ. math. 63, 251–265 (2002). https://doi.org/10.1007/s00010-002-8023-7
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DOI: https://doi.org/10.1007/s00010-002-8023-7