次数大于2的多项式的随机复解析动力系统的JULIA集的连通性

Connectedness of Julia sets for the random dynamical system generated by polynomials of degree≥2

对于复向量序列a_n,我们考虑d次多项式F_n:=f_a_n ·……·f_a序列(F_n).Fatou集F_a定义为扩充平面上使得F_n正规的点z的全体,其余集J_a称为Julia集.该文的目的是对于有界的序列(a_n)研究J_a_n的连通性.二次随机复动力系统的一些已知结果推广到一般情形.

For a sequence (an) of complex vectors we consider the polynomials of d degree and the sequence ( Fn ) of iterates Fn: = fan ...... ofan . The Fatou set F(an) is by definition the set of all z C such that ( Fn) is normal in some neighborhood of z ,while the complement of F(an) is called the Julia set J(an),. Hie aim of this paper is to study the connectedness of the Julia set J(an) for the bounded sequence. Some known results on the quadratic random dynamical system are extended to the general case.