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

2026/03/17 by David Nikitin, Nataliya Stankevich · 1 voice
Mathematics · Physics and Astronomy · #math.NA #nlin.CD

paper · pdf · doi:10.48550/arxiv.2603.16174

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.

Discussions

• David Nikitin, Nataliya Stankevich: Effect of machine arithmetic errors for multi-turn invariant curve destruction https://arxiv.org/abs/2603.16174 https://arxiv.org/pdf/2603.16174 https://arxiv.org/h [bsky, 0 points, 0 comments]

Related

• A note on a standard family of twist maps
• Computational Geometry Column 38
• A KAM type theorem for systems with round-off errors
• The Complete Intersection Discrepancy of a Curve I: Numerical Invariants
• Numerically Invariant Signature Curves