Interpolation of power mappings

• Jack Burkart ^[1] ; Kirill Lazebnik ^[2]
  1. [1] University of Wisconsin–Madison

     University of Wisconsin–Madison

     City of Madison, Estados Unidos

     
  2. [2] University of North Texas

     University of North Texas

     Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 3, 2023, págs. 1181-1200
• Idioma: inglés
• DOI: 10.4171/RMI/1359
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• Resumen

  • Let .Mj /1 jD1 2 N and .rj /1 jD1 2 RC be increasing sequences satisfying some mild rate of growth conditions. We prove that there exists an entire function f WC ! C whose behavior in the large annuli ¹z 2 C W rj exp. =Mj / jzj rjC1º is given by a perturbed rescaling of z 7! zMj , such that the only singular values of f are rescalings of ˙r Mj j . We describe several applications to the dynamics of entire functions