2022/08/01 by Hu, Mi · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2208.00546
In this paper, we investigate the precise behavior of orbits inside attracting basins. Let f be a holomorphic polynomial of degree m≥2 in ℂ, \mathcal A(p) be the basin of attraction of an attracting fixed point p of f, and Ωi (i=1, 2, ⋯) be the connected components of A(p). We prove that there is a constant C so that for every point z0 inside any Ωi, there exists a point q∈ ∪k f-k(p) inside Ωi such that dΩi(z0, q)≤ C, where dΩi is the Kobayashi distance on Ωi.