Hyperbolic trajectories of time discretizations
The authors investigate the hyperbolic trajectories of time discretizations. They address the problem of persistence of the trajectories of time discretizations. Conditions which guarantee the existence of a mirror trajectory for the underling vector field are given. Estimates are provided for the important quantities in terms of the problem parameters. In addition the Lyapunov-Perron method is implemented as a numerical algorithm for stable/unstable manifolds of fixed points. The authors also provide the foundation for a rigorous implementation of the Lyapunov-Perron method for computing the trajectories, for example periodic orbits.
scientific article; zbMATH DE number 2117565
scientific article