Effect of machine arithmetic errors for multi-turn invariant curve destruction

TL;DR

This paper investigates how machine arithmetic errors can cause the destruction of multi-turn invariant curves in dynamical systems, highlighting that increased numerical precision can prevent such artifacts.

Contribution

It demonstrates that numerical artifacts from machine precision errors can lead to false destruction of invariant curves, and increasing precision can mitigate this issue.

Findings

Destruction of invariant curves can be caused by numerical artifacts.

Higher machine precision reduces the occurrence of artifacts.

Artifacts depend on the precision of machine arithmetic.

Abstract

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.