Interior dynamics of fatou sets

Abstract In this paper, we investigate the precise behavior of orbits inside attracting basins. Let f be a holomorphic polynomial degree $$m\ge 2$$ m ≥ 2 in $$\mathbb {C}$$ C , $$\mathcal {A}(p)$$ A ( p ) basin attraction an fixed point p and $$\Omega _i (i=1, 2, \cdots )$$ Ω i = 1 , ⋯ connected components . Assume _1$$ contains $$\{f^{-1}(p)\}\cap \Omega _1\ne \{p\}$$ { f - } ∩ ≠ Then there is constant C so that for every $$z_0$$ z 0 any _i$$ exists $$q\in \cup _k f^{-k}(p)$$ q ∈ ∪ k such $$d_{\Omega _i}(z_0, q)\le C$$ d ≤ where _i}$$ Kobayashi distance on _i.$$ . paper Hu (Dynamics parabolic basins, 2022), proved result not valid