Dynamics of numerical approximations
The perturbation of hyperbolic invariant sets of dynamical systems are studied when the system is approximated numerically. A result by \textit{B. Fiedler} and \textit{J. Scheurle} [Discretization of homoclinic orbits \dots, Mem. Am. Math. Soc. 570, 79p. (1996)] is used stating that the numerically approximated flow is the exact flow of some perturbed system. This is used to obtain results on the behavior of equilibrium points, periodic orbits, and tori under discretization in time. Results on the preservation of structural stability for gradient systems are presented. The last section gives open problems.
scientific article; zbMATH DE number 1183183
scientific article