Effect of machine arithmetic errors for multi-turn invariant curve destruction
This addresses a specific numerical stability issue in dynamical systems simulations, but it is incremental as it focuses on a particular map and artifact.
The study investigated how machine arithmetic errors affect the destruction of multi-turn invariant curves in the three-dimensional Mira map, finding that local multiple bends can cause destruction and that increasing arithmetic accuracy avoids numerical artifacts.
Using the example of three-dimensional Mira map, it is shown that the destruction of a multi-turn invariant curve can occur through the appearance of local multiple bends. It was found that, depending on the precision of machine arithmetic, a complication of the multi-turn invariant curve can be observed, which is a numerical artifact. Artifact can be avoided with increasing of machine arithmetic accuracy.