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| We consider a continuous time non-autonomous dynamical system having two hyperbolic bounded trajectories that converge towards each other. Applying a one-step-method with sufficiently small step size we get hyperbolic bounded trajectories of the discretized system. They lie in a small neighborhood of the original trajectories and are also homoclinic.
For verifying our error estimates, we construct an example in continuous time with known homoclinic trajectories. An illustration of homoclinic dynamics can be achieved by computing stable and unstable fiber bundles. For this task, an algorithm of England, Krauskopf and Osinga is introduced that we generalize to the non-autonomous case. |
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