Solutions of equivariance for iterative differential equations Original Research Article

By equivariance under the action of a group of invertible linear transformations on a Euclidean space, we describe symmetries of mappings. Based on known results on existence of solutions for iterative differential equations, in this paper, we discuss the special class of solutions which possess equivariance on R. Existence, uniqueness, and smooth dependence are given by using fixed-point theorems and by virtue of properties of finitely generated Lie groups.