2022/08/07 by Hu, Mi · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2208.03756
In this paper, we investigate the behavior of orbits inside parabolic basins. Let f(z)=z+azm+1+(higher terms), m≥1, a≠0. We choose an arbitrary constant C>0 and a point q∈\bf vj\capPj. Then there exists a point z0∈ Pj so that for any q∈ Q:= ∪l=0∞f-l(fk(q)) (l, k are non-negative integers), the Kobayashi distance d_\mathcal Pj(z0, q)> C, where dPj is the Kobayashi metric. In a previous paper [4], we showed that this result is not valid for attracting basins.