Shadowing in structurally stable flows (Q1377531)

This work is devoted to the study of a flow generated by a system of ODEs on a closed manifold \(M\), in the case that the flow is structurally stable. The author proves that the pseudotrajectories of a structurally stable flow are shadowed by real trajectories, and the shadowing is Lipschitz with respect to the ``error''. The pecularity of the present work is that the hyperbolic structures near rest points and near nonsingular nonwandering trajectories are qualitatively different. Thus, standard shadowing approaches do not work.