Decay of correlations for normally hyperbolic trapping

Resolvent estimates for normally hyperbolic trapped sets

We give pole free strips and estimates for resolvents of semiclassical operators which, on the level of the classical flow, have normally hyperbolic smooth trapped sets of codimension two in phase space. Such trapped sets are structurally stable and our motivation comes partly from considering the wave equation for Kerr black holes and their perturbations, whose trapped sets have precisely this structure. We give applications including local smoothing effects with epsilon derivative loss for the Schrödinger propagator as well as local energy decay results for the wave equation.

关于微局部分解与正规双曲算子Feynman Propagators的构造

On microlocalisation and the construction of Feynman Propagators for normally hyperbolic operators

本文提出全局双曲时空上正规双曲算子的全局微局部分解构造，推广了Duistermaat-Hörmander的Feynman propagators构造，并证明其满足反映Hadamard态存在性的正性性质。

格林算子的极化集：通常超曲面方程

Polarisation sets of Green operators for normally hyperbolic equations

研究通常超曲面方程中格林算子的极化集，通过计算先进和迟滞格林算子及其差的核分布极化集，为相关算子的极化和波前集计算提供方法，并以Proca方程为例填补了近期研究中的空白。

Diffusion along chains of normally hyperbolic cylinders

We develop a geometric mechanism to prove the existence of orbits that drift along a prescribed sequence of cylinders, under some general conditions on the dynamics. This mechanism can be used to prove the existence of Arnold diffusion for large families of perturbations of Tonelli Hamiltonians on $\mathbb{A}^3$. Our approach can also be applied to more general Hamiltonians that are not necessarily convex. The main geometric objects in our framework are $3$-dimensional invariant cylinders with boundary (not necessarily hyperbolic), which are assumed to admit center-stable and center-unstable m…

长时间传播的相干态在正常双曲设置下的行为

Long-time propagation of coherent states in a normally hyperbolic setting

研究在正常双曲设置下，通过WKB态和压缩态描述相干态的长时间传播行为，揭示其局域化特性转变。

Lorentzian 度规的副因果形变与代数量子场论中的 Møller 同构

Paracausal deformations of Lorentzian metrics and Møller isomorphisms in algebraic quantum field theory

本文提出整体双曲度规间的副因果关系，据此构造正规双曲算子解空间的 Møller 同构，并将其提升为保持 Hadamard 波前集的 CCR 代数 *-同构。