For each positive integer k,the radix representation of the complex numbers in the base -k+i gives rise to a lattice self-affine tile T_k in the plane,which consists of all the complex numbers that can be expressed in...For each positive integer k,the radix representation of the complex numbers in the base -k+i gives rise to a lattice self-affine tile T_k in the plane,which consists of all the complex numbers that can be expressed in the form∑_(j≥1)d_j(-k+i)^(-j),where d_j∈{0,1,2,...,k^2}.We prove that T_k is homeomorphic to the closed unit disk{z∈C:|z|≤1}if and only if k≠2.展开更多
基金The first author is supported by Youth Project of Tianyuan Foundation(10226031)zhongshan University Promotion Foundation for Young Teachers (34100-1131206)+1 种基金the second author is supported by National science Foundation(10041005)Guangdong Provic
文摘For each positive integer k,the radix representation of the complex numbers in the base -k+i gives rise to a lattice self-affine tile T_k in the plane,which consists of all the complex numbers that can be expressed in the form∑_(j≥1)d_j(-k+i)^(-j),where d_j∈{0,1,2,...,k^2}.We prove that T_k is homeomorphic to the closed unit disk{z∈C:|z|≤1}if and only if k≠2.
