On the calculation of the linear stability parameter of periodic orbits

TL;DR

This paper introduces an improved, highly accurate method for calculating Henon's stability parameter of periodic orbits using the differential of the Poincare map, surpassing previous methods in accuracy.

Contribution

The paper presents a novel method based on the first variational equation for calculating Henon's stability parameter, improving accuracy over existing techniques.

Findings

The new method provides more accurate stability calculations.

It successfully handles cases where previous methods failed.

Examples demonstrate the method's effectiveness.

Abstract

In this paper we propose an improved method for calculating Henon's stability parameter, which is based on the differential of the Poincare map using the first variational equation. We show that this method is very accurate and give some examples where it gives correct results, while the previous method could not cope.