Bing Mao DENG, Cui Ping ZENG, Dan LIU, De Gui YANG
We studied the normality concerning repelling periodic poits, and obtained two results as follow: (1) Let $\mathcal{F}$ be a family of holomorphic functions in a domain $D$, and let $k\ge 2$ be a positive integer. If, for each $f\in \mathcal{F}$, all zeros of $f(z)-z$ have multiplicity at least $3$, and its iteration $f^k$ has at most $3k-1$ distinct repelling fixed points in $D$, then $\mathcal{F}$ is normal in $D$. There are examples show that all conditions are necessary in this result; (2) Let $\mathcal{F}$ be a family of meromorphic functions in a domain $D$, and let $k\ge 3$ be a positive integer. If, for each $f\in \mathcal{F}$, all zeros and poles of $f(z)-z$ have multiplicity at least $3$, and its iteration $f^k$ has at most $2k-1$ distinct repelling fixed points in $D$, then $\mathcal{F}$ is normal in $D$.
