On The Open Set Condition And The Strong Open Set Condition For A Class Of Self-affine Systems

Let A be a d×d expanding matrix,and suppose that u is a family of orthogonal matrices with Au=uA.We construct the following iterated function systemf_i(x)=Q_iA^-k_i(x+d_i),i=1,2,…,N,where Q_i∈u,d_i∈R^d and k_i∈Z⁺.In this paper,we firstly study the existence of the self-affine set generated by the iterated function system;Then,according to the properties of pseudo-norm w(x)[5],we show that if the system satisfies the open set condition,then the strong open set condition also holds.