一类亚纯函数的Julia集

Julia sets of some meromorphic functions

证明具有多项式Ｓｃｈｗａｒｚ导数的亚纯函数，如果它有一个渐近值为∞（或为极点），那么它的Ｊｕｌｉａ集的Ｈａｕｓｄｏｒｆｆ维数等于２．特别地，具有多项式Ｓｃｈｗａｒｚ导数的整函数，其Ｊｕｌｉａ集的Ｈａｕｓｄｏｒｆｆ维数必为２．

For a meromorphic function with polynomial Schwarzian derivative,if one of its asymptotic values is also a pole or the infinity, then the Hausdorff dimension of its Julia set is two.In particular, the Hausdorff dimension of the Julia set of an entire function with polynomial Schwarzian derivative is equal to two.