The Structure of Strongly Stationary Systems

Stabilizers of Stationary Actions of Lattices in Semisimple Groups

Every stationary action of a strongly irreducible lattice or commensurator of such a latiice in a general semisimple group, with at least one higher-rank connected factor, either has finite stabilizers almost surely or finite index stabilizers almost surely.

The Furstenberg-Zimmer structure theorem for stationary random walks

We prove the following version of the Furstenberg-Zimmer structure theorem for stationary actions: Any stationary action of a locally compact second-countable group is a weakly mixing extension of a measure-preserving distal system.

Recurrence for stationary group actions

Using a structure theorem from [FG2010] we prove a version of multiple recurrence for sets of positive measure in a general stationary dynamical system.

On the isometry group and the geometric structure of compact stationary Lorentzian manifolds

We study the geometry of compact Lorentzian manifolds that admit a somewhere timelike Killing vector field, and whose isometry group has infinitely many connected components. Up to a finite cover, such manifolds are products (or amalgamated products) of a flat Lorentzian torus and a compact Riemannian (resp., lightlike) manifold.

具有 Logistic 增长的空间一维自扩散方程稳态问题的几何结构

Geometric structure of stationary problem for spatial 1D self-diffusion equation with logistic growth

本文利用 Poincaré-Lyapunov 紧化分析含 Logistic 增长的一维非线性自扩散方程稳态 ODE，揭示自扩散系数作为分岔参数如何导致同宿到异宿轨道转变并改变稳态结构。