Dynamics of numerical approximations

摘要

Assuming that a differential equation has a hyperbolic invariant set, we discuss the existence of a similar invariant set for the map defined by a numerical approximation, as well as the closeness of these sets in the C1-topology. Particular emphasis is given to equilibrium points, periodic orbits and invariant tori for the differential equation. We present also a result on the preservation of structural stability for gradient systems.