%0 Journal Article %T A general symmetry preserving reduction scheme and normal form for dynamical systems with a compact symmetry group %A Maria Cristina Ciocci %A Johan Noldus %J Mathematics %D 2004 %I arXiv %X We present a generalized Lyapunov Schmidt reduction scheme for diffeomorphisms living on a finite dimensional real vector space V which transform under real one dimensional characters of an arbitrary compact group with linear action V. Moreover we prove a normal form theorem, such that the normal form still has the desirable transformation properties with respect to the character. %U http://arxiv.org/abs/math/0411510v1