论文标题
共振和相位锁定现象，用于保存圆环图
Resonances and Phase Locking Phenomena for Foliation Preserving Torus Maps
论文作者
论文摘要
以专家的身份闻名，在非线性系统中产生共鸣会导致新的不变对象，从而导致新的行为。 本文的目的是研究在保存圆环图下的共振产生的不变集。那是保留非理性行的叶面$ l_ {θ_{0}} = \ {θ_{0}+ωt| t \ in \ Mathbb {r} \} \ subset \ mathbb {t}^{d} $。 保留地图的叶面自然似乎是对圆环中线性流的重新训练，并且在涉及耦合振荡器，延迟方程，具有移动墙的谐振器等的多种应用中起着重要作用。我们在这里找到的不变对象，导致这些模型行为的预测。 由于本文的结果旨在用于其他问题，因此我们开发了非常定量的结果，从而非常明确地描述了现象和控制它们的不变对象。 用于保存图的叶面的相位锁定区的结构与圆环的通用图大不相同。的确，为了完整，我们对圆环的通用图的情况进行了类似的分析，并表明在叶片中保存地图中出现的对象在定量和质量上与通用圆环图的对象不同。这对应用程序有后果。
It is well known for experts that resonances in nonlinear systems lead to new invariant objects that lead to new behaviors. The goal of this paper is to study the invariant sets generated by resonances under foliation preserving torus maps. That is torus which preserve a foliation of irrational lines $L_{θ_{0}}=\{θ_{0}+Ωt | t\in\mathbb{R}\}\subset\mathbb{T}^{d}$. Foliation preserving maps appear naturally as reparametrization of linear flows in the torus and also play an important role in several applications involving coupled oscillators, delay equations, resonators with moving walls, etc. The invariant objects we find here, lead to predictions on the behavior of these models. Since the results of this paper are meant to be applied for other problems, we have developed very quantitative results giving very explicit descriptions of the phenomena and the invariant objects that control them. The structure of the phase locking regions for foliation preserving maps is very different than for generic maps of the torus. Indeed, for the sake of completeness, we have developed similar analysis for the case of generic maps of the torus and shown that the objects that appear in foliation preserving maps are quantitatively and qualitatively different from those of generic torus maps. This has consequences in applications.
