Two concepts for numerical periodic solutions of ODE's

摘要

In computing a numerical approximation for a hyperbolic periodic orbit of an ordinary differential equation one can look either for periodic points of the mapping corresponding the numerical method or for an invariant set of that mapping. Here the one-step methods are considered. It is shown that both of these concepts for numerical approximation of periodic solutions are meaningful in the sense that the corresponding sets exist and are Ck-circles, provided the method is accurate enough. Also both of these are accurate to the order of the method. Further some relations of these concepts are studied.