Action -梯度极小化伪轨与几乎不变环面
Action-gradient-minimizing pseudo-orbits and almost-invariant tori
摘要：
运输近可积，但部分混乱，$1 1/2$度的自由度的哈密顿系统是由不变环面阻塞，并减少在\emph{almost}不变环面，都与一个相邻的可积系统的不变环面。具有有理旋转数的“几乎不变”环面可以使用周期性\emph{pseudo-orbits}的连续族来定义以使表面叶状，而无理旋转数环面可以通过嵌套这种有理环面的序列来定义。“伪轨道”的三种定义，\emph{action-gradient--minimizing}（ACMin）、\emph{quadratic-flux-minimizing}（QFMin）和\emph{ghost}轨道，基于汉密尔顿原理的变体，使用不同的策略尽可能接近地使作用极端化。等价的拉格朗日（配置空间作用）和哈密顿（相空间作用）的配方，和一种新的方法来可视化的行动最小化和极小极大轨道的基础上AGMin伪轨道。
英文摘要：
Transport in near-integrable, but partially chaotic, $1 1/2$ degree-of-freedom Hamiltonian systems is blocked by invariant tori and is reduced at \emph{almost}-invariant tori, both associated with the invariant tori of a neighboring integrable system. "Almost invariant" tori with rational rotation number can be defined using continuous families of periodic \emph{pseudo-orbits} to foliate the surfaces, while irrational-rotation-number tori can be defined by nesting with sequences of such rational tori. Three definitions of "pseudo-orbit," \emph{action-gradient--minimizing} (AGMin), \emph{quadratic-flux-minimizing} (QFMin) and \emph{ghost} orbits, based on variants of Hamilton's Principle, use different strategies to extremize the action as closely as possible. Equivalent Lagrangian (configuration-space action) and Hamiltonian (phase-space action) formulations, and a new approach to visualizing action-minimizing and minimax orbits based on AGMin pseudo-orbits, are presented.
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