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Solutions of equivariance for a polynomial-like iterative equation

Published online by Cambridge University Press:  11 July 2007

Weinian Zhang
Affiliation:
Department of Mathematics, Sichuan University, Chengdu 610064, People's Republic of China

Abstract

Using fixed point theorems we discuss continuous solutions of Γ-equivariance for a polynomial-like iterative equation on the real line, where Γ is a closed subgroup of the general linear group GL(R). Our main results guarantee the existence of solutions with certain kinds of symmetry. We show that, under restrictive hypotheses, similar results can be proved in a higher-dimensional case, where the symmetry group is a topologically finitely generated subgroup of the group generated by rotations and dilations in N-dimensional Euclidean space.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2000

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