论文标题
Lagrangian分布弱的苛性遗传学
Caustics of weakly Lagrangian distributions
论文作者
论文摘要
我们研究分布的半经典序列$ u_h $与Lagrangian Submanifold相关的相位空间$ \ lag \ subset t^*x $。如果$ u_h $是一种半经典的拉格朗日发行版，它以$ \ \ \ $ \ $的最大速率集中在$ \ \ u_h $上，那么$ u_h $的渐近学对Arnol'd的作品充分理解了，提供了$ \ lag $ project to $ x $的$ x $，并具有稳定的lagrangian Singularity。在更一般的假设下，我们就集中在$ \ lag $上的速度（再次假设稳定的预测）上建立了对$ u_h $的SUP-NORM估算值。这些估计值适用于可集成和kam hamiltonians的本征函数序列。
We study semiclassical sequences of distributions $u_h$ associated to a Lagrangian submanifold of phase space $\lag \subset T^*X$. If $u_h$ is a semiclassical Lagrangian distribution, which concentrates at a maximal rate on $\lag,$ then the asymptotics of $u_h$ are well-understood by work of Arnol'd, provided $\lag$ projects to $X$ with a stable Lagrangian singularity. We establish sup-norm estimates on $u_h$ under much more general hypotheses on the rate at which it is concentrating on $\lag$ (again assuming a stable projection). These estimates apply to sequences of eigenfunctions of integrable and KAM Hamiltonians.
