论文标题
普遍的行为，几乎可以肯定的是使用不变的k-cones平滑流动的庞加雷 - 弯曲定理
Prevalent behavior and almost sure Poincare-Bendixson Theorem for smooth flows with invariant k-cones
论文作者
论文摘要
我们从衡量k k的平滑流量的度量理论的角度研究了全局动力学。对于此类系统，可以表明，普遍（或等效地，几乎所有）轨道将被伪订购或收敛到平衡。如果等级k = 1，这将减少到赫希普遍存在的收敛定理；并暗示了Case K = 2的几乎纯净的Poincare-Bendixson定理。然后，将这些结果应用于获得高维微分方程的几乎确定的庞贝 - 弯曲定理。
We investigate the global dynamics from a measure-theoretic perspective for smooth flows with invariant cones of rank k. For such systems, it is shown that prevalent (or equivalently, almost all) orbits will be pseudo-ordered or convergent to equilibria. This reduces to Hirsch's prevalent convergence Theorem if the rank k=1; and implies an almost-sure Poincare-Bendixson Theorem for the case k=2. These results are then applied to obtain an almost sure Poincare-Bendixson theorem for high-dimensional differential equations.
