论文标题
哈密顿系统中瞬时运动的测量，维度和复杂性
Measure, dimension, and complexity of the transient motion in Hamiltonian systems
论文作者
论文摘要
在相空间中开放，泄漏或包含孔的Hamiltonian系统具有最终逃脱系统域的解决方案。在越过逃生阈值之前，这种逃生轨道描述的运动可以理解为瞬态行为。在这项工作中，我们引入了一种数值方法，可以在视觉上说明和量化哈密顿系统中的瞬态运动，该系统基于瞬态度量，这是自然措施的有限时间版本。我们将此方法应用于两个物理系统：由符号映射描述的单个无用的转移tokamak；以及由平面循环限制的三体问题建模的地球系统。我们的结果描绘了初始条件集合的不同位置如何导致两个系统中的不同瞬态动态场景。我们表明，可以从几何方面，瞬态相关维度和动态方面（瞬态复杂性系数）正确量化这些情况。
Hamiltonian systems that are either open, leaking, or contain holes in the phase space possess solutions that eventually escape the system's domain. The motion described by such escape orbits before crossing the escape threshold can be understood as a transient behavior. In this work, we introduce a numerical method to visually illustrate and quantify the transient motion in Hamiltonian systems based on the transient measure, a finite-time version of the natural measure. We apply this method to two physical systems: the single-null divertor tokamak, described by a symplectic map; and the Earth-Moon system, as modeled by the planar circular restricted three-body problem. Our results portray how different locations for the ensemble of initial conditions may lead to different transient dynamical scenarios in both systems. We show that these scenarios can be properly quantified from a geometrical aspect, the transient correlation dimension, and a dynamical aspect, the transient complexity coefficient.
