Speeds of convergence for petals of semigroups of holomorphic functions


  • Maria Kourou Julius-Maximilians Universität Würzburg, Department of Mathematics
  • Konstantinos Zarvalis Aristotle University of Thessaloniki, Department of Mathematics


One-parameter semigroup of holomorphic functions, spectral value, backward orbit, repelling fixed point, petal


We study the backward dynamics of one-parameter semigroups of holomorphic self-maps of the unit disk. More specifically, we introduce the speeds of convergence for petals of the semigroup, namely the total, orthogonal, and tangential speeds. These are analogous to speeds of convergence introduced by Bracci, yet profoundly different due to the nature of backward dynamics. Results are extracted on the asymptotic behavior of speeds of petals, depending on the type of the petal. We further discuss the asymptotic behavior of the hyperbolic distance along non-regular backward orbits.



How to Cite

Kourou, M., & Zarvalis, K. (2024). Speeds of convergence for petals of semigroups of holomorphic functions. Annales Fennici Mathematici, 49(1), 119–134. https://doi.org/10.54330/afm.143723