摘要
It is proved in this paper that the union of escaping parameter rays without endpoints for the cosine family Sκ(z)=eκ(ez+e-z),whereκ∈C is a parameter,has Hausdorff dimension 1,which implies that the ray endpoints alone have Hausdorff dimension 2.This shows that Karpińska’s dimension paradox occurs also in the parameter plane of the cosine family.
基金
the National Natural Science Foundation of China(Nos.11671091,11731003,11771090)
the Natural Science Foundation of Shanghai(No.17ZR1402900)
the Science and Technology Foundation of Jiangxi Education Department(No.GJJ180944)。
