Alsedà-Misiurewicz systems with place-dependent probabilities

Random iteration with place dependent probabilities

Markov chains arising from random iteration of functions $S_θ:X\to X$, $θ\in Θ$, where $X$ is a Polish space and $Θ$ is arbitrary set of indices are considerd. At $x\in X$, $θ$ is sampled from distribution $θ_x$ on $Θ$ and $θ_x$ are different for different $x$. Exponential convergence to a unique invariant measure is proved. This result is applied to case of random affine transformations on ${\mathbb R}^d$ giving existence of exponentially attractive perpetuities with place dependent probabilities.

位置依赖的幂等迭代函数系统的不变测度

Invariant measures for place dependent idempotent iterated function systems

该研究针对紧度量空间上的位置依赖幂等迭代函数系统，利用Mañé势、Aubry集等动力系统方法刻画了不变幂等概率的密度，并给出一类模糊迭代函数系统吸引子的新公式。

零温下Gibbs概率的大偏差与迭代函数系统的不变幂等概率

Large deviation for Gibbs probabilities at zero temperature and invariant idempotent probabilities for iterated function systems

该文研究一致压缩迭代函数系统相关的Gibbs概率族在零温极限下的大偏差原理，建立其偏差函数与不变幂等概率密度的关联，并借助Mañé势和Aubry集完成偏差函数的刻画。

Transmission and Reflection in the Stadium Billiard: Time-dependent asymmetric transport

We investigate the transmission and reflection survival probabilities for the chaotic stadium billiard with two holes placed asymmetrically. Classically, these distributions are shown to have algebraic or exponential decays depending on the choice of injecting hole and exact expressions are given for the first time and confirmed numerically. As there is no reported quantum theoretical or experimental analogue we propose a model for experimental observation of the asymmetric transport using semiconductor nano-structures and comment on the relevant quantum time-scales.