Ergodicity of hard spheres in a box

球面和圆盘上展现遍历性或涌现性的解析伪旋转

Analytic pseudo-rotations displaying ergodicity or emergence on the sphere and disk

本文在球面和圆盘上构造了具有遍历性或最大阶局部涌现性的解析伪旋转，其方法基于Anosov-Katok共轭逼近原理及Berger引入的相关原理。

解析辛映射在球面、圆柱体和圆盘上显示最小的遍历性

Analytic symplectomorphisms displaying minimal ergodicity on the sphere, cylinder and disk

本文提出了一种在不同几何体上构造具有最小遍历性的解析辛映射的方法，通过推广Berger的原则实现仅3个遍历测度的构造。

Ergodicity properties of $p$ -adic $(2,1)$-rational dynamical systems with unique fixed point

We consider a family of $(2,1)$-rational functions given on the set of $p$-adic field $Q_p$. Each such function has a unique fixed point. We study ergodicity properties of the dynamical systems generated by $(2,1)$-rational functions. For each such function we describe all possible invariant spheres. We characterize ergodicity of each $p$-adic dynamical system with respect to Haar measure reduced on each invariant sphere. In particular, we found an invariant spheres on which the dynamical system is ergodic and on all other invariant spheres the dynamical systems are not ergodic.

Ergodicity criteria for non-expanding transformations of 2-adic spheres

In the paper, we obtain necessary and sufficient conditions for ergodicity (with respect to the normalized Haar measure) of discrete dynamical systems $<f;\mathbf S_{2^{-r}}(a)>$ on 2-adic spheres $\mathbf S_{2^{-r}}(a)$ of radius $2^{-r}$, $r\ge 1$, centered at some point $a$ from the ultrametric space of 2-adic integers $\mathbb Z_2$. The map $f\colon\mathbb Z_2\to\mathbb Z_2$ is assumed to be non-expanding and measure-preserving; that is, $f$ satisfies a Lipschitz condition with a constant 1 with respect to the 2-adic metric, and $f$ preserves a natural probability measure on $\mathbb Z_2$,…

Quantum Ergodicity and Averaging Operators on the Sphere

We prove quantum ergodicity for certain orthonormal bases of $L^2(\mathbb{S}^2)$, consisting of joint eigenfunctions of the Laplacian on $\mathbb{S}^2$ and the discrete averaging operator over a finite set of rotations, generating a free group. If in addition the rotations are algebraic we give a quantified version of this result. The methods used also give a new, simplified proof of quantum ergodicity for large regular graphs.

等谱联络、标架流的遍历性以及球面之间的多项式映射

Isospectral connections, ergodicity of frame flows, and polynomial maps between spheres

本文证明闭负曲率流形上Bochner Laplacian的谱在低秩条件下决定向量丛同构类与联络的规范类，并证明无和乐约化的低秩标架流是遍历的，核心方法是建立其与球面间多项式映射分类的联系。