Resumen de Algebraic approach to equivariance of solutions for an iterative equation
W. Zhang, Bing Xu
Describing the symmetry of a mapping by equivariance with respect to a lin- ear transformation group, the reference [Proc. Roy. Soc. Edinburgh A130 (2000), 1153{1163] gave the existence of equivariant solutions of the polynomial-like iterative equation under the action of topologically ¯nitely generated subgroups of GL(R) on R and the orthogonal group O(N) on RN (N ¸ 2). In this paper, based on the algebraic structure of closed subgroups of GL(R), we prove the equivariance of solutions on R with respect to closed subgroups of GL(R) and extend the result of O(N)-equivariance of solutions to the group O(N) £ hcINi on RN.
