摘要
对于首一多项式P(z)=zn+a1zn-1+…+an,n≥2,F是其Julia集,P.Bhattacharyya和Y.E.Arumaraj[1]猜测d(F)≥2,这里d(F)表示F的直径.本文中,我们将证明对于复平面上任何紧E有不等式d(E)≥2·cap(E)成立,这里cap(E)表示E的对数容量[1],作为推论,我们证明了上述猜测.
For any monic polynomial p(z)= z ̄n + a_1z ̄(ng1) + … + a_n,n≥2,F is the Julia set, P.Bhattacharyya and Y. E. Arumaraj[1] conjectured d (F) ≥2,where d (F) is the diameter ofF. In this note. We will prove d(E)≥2. cap(E)for any compact set E on a,cap(E) isthe logarithemic capacity of E. As a corollary, we prove the above conjecture.