Group actions on one-manifolds, II: Extensions of Hölder's Theorem

具有自治极限的非自治系统紧化的$C^{k}$延拓与不变流形

$C^{k}$ extension and invariant manifolds for the compactification of nonautonomous systems with autonomous limits

针对具有自治极限的非自治系统紧化的高阶光滑性需求，该研究给出了$C^{k}$（$k\neq 2$）延拓判据，并证明了紧化后系统一般紧不变集的中心及中心-稳定流形的存在唯一性。

非平稳正交坐标在佩辛稳定流形邻域中的应用

Non-stationary normal coordinates on neighborhoods of Pesin stable manifolds

本文提出在佩辛稳定流形邻域内构造非平稳正交坐标，用于描述光滑动力系统中稳定和不稳定叶的分形几何结构。

Realisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifolds

We prove that the family of measured dynamical systems which can be realised as uniquely ergodic minimal homeomorphisms on a given manifold (of dimension at least two) is stable under measured extension. As a corollary, any ergodic system with an irrational eigenvalue is isomorphic to a uniquely ergodic minimal homeomorphism on the two-torus. The proof uses the following improvement of Weiss relative version of Jewett-Krieger theorem: any extension between two ergodic systems is isomorphic to a skew-product on Cantor sets.

Equilibrium measures for certain isometric extensions of Anosov systems

We prove that for the frame flow on a negatively curved, closed manifold of odd dimension other than 7, and a Holder continuous potential that is constant on fibers, there is a unique equilibrium measure. We prove a similar result for automorphisms of the Heisenberg manifold fibering over the torus. Our methods also give an alternate proof of Brin and Gromov's result on the ergodicity of these frame flows.

Burgers方程惯性流形的光滑性

Smoothness of Inertial Manifold for the Burgers Equation

本文研究Burgers方程惯性流形的光滑扩展，通过新框架证明其长期行为可由显式光滑一阶ODE确定，提出构造C^{n,ε}光滑扩展的充分条件。

Symbolic extensions for 3-dimensional diffeomorphisms

We prove that every $\mathcal{C}^{r}$ diffeomorphism with $r>1$ on a three-dimensional manifold admits symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. This answers positively a conjecture of Downarowicz and Newhouse in dimension three.