涉及重整化变换的有理函数族的 Fatou 集

摘要

主要研究了涉及重整化变换的一族有理函数 Tnλ Fatou 分支的拓扑性质。事实上，若 D 是有理函数Tnλ的任意1个 Fatou 分支，对任意的参数λ∈R 与 n >1，探讨了 D 与 John 区域的联系。所得结果给出了重整化变换的 Julia 集 J（Tnλ）拓扑复杂性的一个详细刻画。%The topological properties about the Fatou sets of a family of rational maps Tnλ concerning renormalization transformation are mainly studied. In fact,let D be any Fatou component of Tnλ the relations between the John do-main and D are investigated. Hence a perfect topological description of the Julia sets J(Tnλ)about the topological complexity is given.