Global rigidity for totally nonsymplectic Anosov Z^k actions

Totally non-symplectic Anosov actions on tori and nilmanifolds

We show that sufficiently irreducible totally non-symplectic Anosov actions of higher rank abelian groups on tori and nilmanifolds are smoothly conjugate to affine actions.

从图流形上的伪Anosov流到完全周期性流

From pseudo-Anosov flows on graph manifolds to totally periodic flows

研究显示图流形上的伪Anosov流可通过构造部分Birkhoff截面，几乎等价于完全周期性伪Anosov流或悬垂Anosov流，结合先前工作证明图流形上的Transitive Anosov流几乎等价于悬垂Anosov流。

Classification and rigidity of totally periodic pseudo-Anosov flows in graph manifolds

In this article we analyze totally periodic pseudo-Anosov flows in graph three manifolds. This means that in each Seifert fibered piece of the torus decomposition, the free homotopy class of regular fibers has a finite power which is also a finite power of the free homotopy class of a closed orbit of the flow. We show that each such flow is topologically equivalent to one of the model pseudo-Anosov flows which we constructed in a previous article. A model pseudo-Anosov flow is obtained by glueing standard neighborhoods of Birkhoff annuli and perhaps doing Dehn surgery on certain orbits. We als…

On classification of higher rank Anosov actions on compact manifold

We prove global smooth classification results for TNS totally Anosov Z^k actions on general compact manifolds, under each one of the following conditions: joint integrability, resonance-free or Lyapunov pinching condition. Unlike the previous results, we do not require any uniform quasiconformality or pinching condition of action elements on coarse Lyapunov distributions, nor do we have any restriction on the dimension of coarse Lyapunov distributions. The main novelty is in proving a new standard form of the derivative cocycle for any TNS totally Anosov Z^k action on general manifold. A main …

Anosov流乘积的时间变换的刚性现象

Rigidity phenomena for time changes of products of Anosov flows

研究Anosov流乘积的时间变换的刚性，证明具有相同周期轨道稳定子的时间变换共轭于自同构，以及若周期轨道稳定子可同时对角化则时间变换共轭于流乘积，并应用于3维流形上的C^1时间变换。

局部紧群自同态的阴影性与双曲性

Shadowing and Hyperbolicity for Endomorphisms of Locally Compact Groups

利用左一致性，研究局部紧群连续自同态的阴影性，对李群给出无穷小刻画：自同态有阴影性当且仅当其微分是双曲的，并推导出拓扑扩张、正扩张、拓扑Anosov等性质的等价性。