aequationes mathematicae

, Volume 63, Issue 3, pp 251–265

Multivariate Böttcher equation for polynomials with non-negative coefficients

  • O. D. Jones

DOI: 10.1007/s00010-002-8023-7

Cite this article as:
Jones, O. Aequ. math. (2002) 63: 251. doi:10.1007/s00010-002-8023-7


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 \( -\lambda^{-n} \log f^{n}(x) \).

Keywords. Multivariate Böttcher equation, functional iteration, projective distance, non-negative matrix, topical function, multitype branching process.

Copyright information

© Birkhäuser Verlag, Basel, 2002

Authors and Affiliations

  • O. D. Jones
    • 1
  1. 1.Faculty of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, U.K.UK