指示函数检测衰减法向双曲不变流形上的切向瞬态行为
Indicator Functions Detect Tangentially Transient Behaviour on Decaying Normally Hyperbolic Invariant Manifolds
AI总结：
本文研究三自由度哈密顿系统中余维2 NHIM在扰动下失去法向双曲性的衰减过程，通过Poincaré映射和时间延迟函数追踪其衰减，并揭示切向瞬态效应在指示函数中的编码方式。
摘要：
我们研究在不断增加的扰动下，当NHIM失去其法向双曲性时，三自由度哈密顿系统中余维2 NHIM的衰减情景。一方面，我们在Poincaré映射中追踪NHIM内部动力学的衰减。另一方面，我们也在系统相空间中的2维平面上计算时间延迟函数，并追踪其中的衰减。此外，我们观察切向瞬态效应对衰减NHIM的作用及其在延迟时间指示函数中的表现。由此，我们获得了关于NHIM的衰减和切向瞬态效应如何被编码在指示函数中的认识。作为演示示例，我们使用受扰磁偶极子场中电子的运动。
英文摘要：
We study the decay scenario of a codimension-2 NHIM in a three degrees of freedom Hamiltonian system under increasing perturbation when the NHIM loses its normal hyperbolicity. On one hand, we follow this decay in the Poincaré map for the internal dynamics of the NHIM. On the other hand, we also follow the decay in a time delay function calculated on a 2-dimensional plane in the phase space of the system. In addition, we observe the role of tangential transient effects on the decaying NHIM and their manifestation in the delay time indicator function. Thereby we obtain ideas on how the decay of NHIMs and the tangential transient effects are encoded in indicator functions. As an example of demonstration, we use the motion of an electron in a perturbed magnetic dipole field.
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