General linear methods: connection to one step methods and invariant curves

SummaryWe generalize a result of Kirchgraber (1986) on multistep methods. We show that every strictly stable general linear method is essentially conjugate to a one step method of the same order. This result may be used to show that general properties of one step methods carry over to general linear methods. As examples we treat the existence of invariant curves and the construction of attracting sets.