发表机构
School of Physics and Technology, University of Jinan（济南大学物理科学与技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出滑动窗口频率比（SWFR）方法，仅利用径向和极向转折事件计数，在相对论轨道中识别混沌轨道对共振的瞬态访问，并通过克尔、磁化克尔及史瓦西-梅尔文时空的实例验证了其有效性。
AI 中文摘要
长时间庞加莱截面将混沌轨道展平为一片静态模糊，抹去了轨道访问其自身局部结构的顺序。我们引入滑动窗口频率比（SWFR），仅由径向和极向转折事件构建，以恢复沿单条相对论轨道的这一顺序。每个窗口跨越固定数量的径向周期，并简单地统计窗口内的极向事件；由于保留了事件时间，任何候选区间都可以被切出并重新绘制为其自身的庞加莱截面。无需频谱、无需参考中心、无需基函数。可积的克尔基准恢复了已知的频率比，对于具有一致有界计数偏差的规则运动，计数误差界按 $O(W^{-1})$ 衰减。同样的计数随后在混沌中发挥作用。在磁化克尔时空中，一条带电轨道先停留在 $3/5$ 附近，随后停留在 $4/7$ 附近，且正是这些区间展开为五重和七重截面结构；另一条轨道停留在 $1/2$ 附近并具有两个瓣。在史瓦西-梅尔文时空中，一个光子跨越五重图案保持 $4/5$。在每种情况下，截面恰好覆盖了 SWFR 选择的区间：整数计数和相空间几何一致表明，一条全局混沌轨道正在临时访问一个共振。
英文摘要
A long-time Poincaré section flattens a chaotic orbit into one static blur, erasing the order in which the orbit visits its own local structures. We introduce the sliding-window frequency ratio (SWFR), built from nothing but radial and polar turning events, to recover that order along individual relativistic orbits. Each window spans a fixed number of radial cycles and simply counts the polar events inside it; because event times are kept, any candidate interval can be sliced out and replotted as its own Poincaré section. No spectrum, no reference center, no basis functions. Integrable Kerr benchmarks recover the known frequency ratios, and for regular motion with uniformly bounded count deviations the counting-error bound falls off as $O(W^{-1})$. The same counts then pay off in chaos. In magnetized Kerr spacetime a single charged orbit dwells near $3/5$ and later near $4/7$, and exactly those intervals open into fivefold and sevenfold section structures; a second orbit dwells near $1/2$ with two lobes. In Schwarzschild--Melvin spacetime a photon holds $4/5$ across a fivefold pattern. In every case the section covers exactly the interval SWFR selected: integer counts and phase-space geometry agree that a globally chaotic orbit is paying a temporary visit to a resonance.
Comments18 pages, 6 figures
