典型域上的全纯自映射迭代

Iteration of Holomorphic Self-maps in Classical Domain

证明如果 f是第一类典型域RI 到RI 的无固定点的全纯映射 ,且 f(Bnm) Bnm则映射簇 { fn}的任一收敛子列收敛于RI 和Bnm的公共边界上的一点 .其中 fn 是f的n次迭代 .

Proved here is the theorem, that, if fis the holomo rp hic self-map in H(R I;R I) without fixed point in the first classical domain R I and if f(B nm ) nm , each convergent sub-array of map cluster {f n} iterat es at a point on the conjunct boundary of R I and B nm , where f n is the nth iteration of f .