Holomorphic Box Mappings

摘要

Box mappings were introduced as a tool for studying the dynamics of real unimodalpolynomials. In the same paper, the main property of growing moduli was proved. This generalized earlier results obtained for certain ratios on the real line. In the paper, the authors present a more general result with a slightly different proof, not more complicated that the original proof of a weaker result. The generalization consists in allowing a large class of holomorphic box mappings without any connection with real dynamics. The result also generalizes the estimate used for the purpose of constructing quasiconformal conjugacies between quadratic polynomials, not necessarily real.