An improved theory of asymptotic unfoldings

An asymptotic unfolding of a dynamical system near a rest point is a system with additional parameters, such that every one-parameter deformation of the original system can be embedded in the unfolding preserving all properties that can be detected by asymptotic methods. Asymptotic unfoldings are computed using normal (and hypernormal) form methods. We present a simplified and improved method of computing such unfoldings that can be used in any normal form style.