Multivariate Böttcher equation for polynomials with non-negative coefficients |
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Authors: | O D Jones |
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Institution: | Faculty of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, U.K., UK
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Abstract: | Summary. We give conditions for the multivariate Böttcher equation b(f (x)) = b(x)l \beta(f (x)) = \beta(x)^{\lambda} to have a solution, in the case where f : \mathbbRd ? \mathbbRd 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 -l-n logfn(x) -\lambda^{-n} \log f^{n}(x) . |
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