Lefranc Marc
Laboratoire de Physique des Lasers, Atomes, Molécules, UMR CNRS 8523, Centre d'Etudes et de Recherches Lasers et Applications, Université des Sciences et Technologies de Lille, F-59655 Villeneuve d'Ascq, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Sep;74(3 Pt 2):035202. doi: 10.1103/PhysRevE.74.035202. Epub 2006 Sep 13.
The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proven to be a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core principles upon which this approach is built--determinism and continuity--apply in any dimension. We propose an alternative framework in which these principles are enforced on triangulated surfaces rather than curves, and we show that in dimension 3 our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map.
基于不稳定周期轨道的纽结理论表征对混沌进行拓扑分析已被证明是一种强大的方法，然而纽结理论仅适用于三维系统。尽管如此，构建此方法的核心原则——确定性和连续性——在任何维度上都适用。我们提出了一种替代框架，其中这些原则在三角剖分曲面上而非曲线上得到应用，并且我们表明在三维情况下，我们的方法通过数值预测出马蹄映射周期轨道的正确拓扑熵。
