论文标题
哈密顿流动的非均匀的沿着甲基二元特性具有影响
Non-uniform ergodic properties of Hamiltonian flows with impacts
论文作者
论文摘要
两个未耦合振荡器的恒星特性，一个水平和垂直的振荡器，驻留在一类非矩形的星形多边形中，仅研究了垂直和水平边界，并研究了从其边界产生弹性的影响。我们证明，ISO-Energy级别设置拓扑的拓扑会在非琐碎的情况下变化。水平集的流动始终与翻译表面上的翻译流相结合，但是，对于部分能量的某些段，表面的属严格大于一个。当至少一个振荡器是非谐波的，或者两者都是谐波和非谐音时，我们证明，对于包括影响力的所有局部能量，几乎所有局部能量时，水平集合的流量都是独特的。当两个振荡器都是谐波和共鸣时，我们证明存在部分能量的间隔，在哪些周期性丝带和其他千古组件共存。我们证明，对于此类段的几乎所有部分能量，运动在不被周期性丝带所占据的水平集的部分都是独特的。这意味着Ergodic平均项目可以在配置空间中将平滑加权平均值分组。
The ergodic properties of two uncoupled oscillators, a horizontal and vertical one, residing in a class of non rectangular star-shaped polygons with only vertical and horizontal boundaries and impacting elastically from its boundaries are studied. We prove that the iso-energy level sets topology changes non-trivially; the flow on level sets is always conjugated to a translation flow on a translation surface, yet, for some segments of partial energies the genus of the surface is strictly larger than one. When at least one of the oscillators is un-harmonic, or when both are harmonic and non-resonant, we prove that for almost all partial energies, including the impacting ones, the flow on level sets is unique ergodic. When both oscillators are harmonic and resonant, we prove that there exist intervals of partial energies on which periodic ribbons and additional ergodic components co-exist. We prove that for almost all partial energies in such segments the motion is unique ergodic on the part of the level set that is not occupied by the periodic ribbons. This implies that ergodic averages project to piecewise smooth weighted averages in the configuration space.
