半共轭于可数分支分段凸映射的不连续系统的拟紧性与统计性质

均匀流的不变分布

Invariant Distributions for homogeneous flows

我们证明了有限体积齐次流形上的每一个齐次流都有可数个独立的不变分布，除非它与环面上的线性流共轭。我们还证明了同样的结论适用于齐次空间的任何不与环面平移共轭的仿射变换。作为证明的一部分，我们有任何光滑的部分双曲流在任何紧流形有可数许多不同的极小集，因此可数许多不同的遍历概率测度。因此，卡托克和格林菲尔德-瓦拉赫猜想在上述所有情况下都成立。

半 conjugate 于预分段凸或扩张映射的系统统计稳定性研究

Statistical stability for systems semi-conjugate to pre-piecewise \textit{convex or expanding} maps with countably many branches

本文研究半 conjugate 于预分段凸或扩张映射的系统统计稳定性，提出一般条件保证未扰动测度在适当拓扑下连续，并给出测度连续模的定量估计。

Constant Slope Maps on the Extended Real Line

For a transitive countably piecewise monotone Markov interval map we consider the question whether there exists a conjugate map of constant slope. The answer varies depending on whether the map is continuous or only piecewise continuous, whether it is mixing or not, what slope we consider, and whether the conjugate map is defined on a bounded interval, half-line or the whole real line (with the infinities included).

具有可数分支的分段凸映射的 Frobenius-Perron 算子的拟紧性

Quasi-compactness of Frobenius-Perron Operator for Piecewise Convex Maps with Countable Branches

本文利用 Lasota-Yorke 不等式证明了具有可数无穷分支的分段凸映射的 Frobenius-Perron 算子的拟紧性，并确立了其绝对连续不变测度的存在性及系统的强遍历性质。

Constant Slope Models for Finitely Generated Maps

We study countably monotone and Markov interval maps. We establish sufficient conditions for uniqueness of a conjugate map of constant slope. We explain how global window perturbation can be used to generate a large class of maps satisfying these conditions.

Constant slope maps and the Vere-Jones classification

We study continuous countably piecewise monotone interval maps, and formulate conditions under which these are conjugate to maps of constant slope, particularly when this slope is given by the topological entropy of the map. We confine our investigation to the Markov case and phrase our conditions in the terminology of the Vere-Jones classification of infinite matrices.