低维赤道的随机矩阵乘积的最大李雅普诺夫指数的赫尔德正则性

Nonexistence of Lyapunov Exponents for Matrix Cocycles

It follows from Oseledec Multiplicative Ergodic Theorem that the Lyapunov-irregular set of points for which the Oseledec averages of a given continuous cocycle diverge has zero measure with respect to any invariant probability measure. In strong contrast, for any dynamical system $f:X\rightarrow X$ with exponential specification property and a H$\ddot{\text{o}}$lder continuous matrix cocycle $A:X\rightarrow G (m,\mathbb{R})$, we show here that if there exist ergodic measures with different Lyapunov spectrum, then the Lyapunov-irregular set of $A$ is residual (i.e., containing a dense $G_δ$ set…

具有简单最大李雅普诺夫指数的随机矩阵乘积的极限定理

Limit theorems for random matrix products with a simple top Lyapunov exponent

该研究针对具有指数矩和简单最大李雅普诺夫指数的独立同分布随机矩阵乘积，在不假设不可约性的情况下，建立了赤道外的收缩性与谱间隙，得到了中心极限定理等极限结果，其收缩准则还可推广至部分随机映射。

不变函数正则性的数值界：动态环境中高尔顿-沃森过程的灭绝概率

Numerical bounds on the regularity of an invariant function: Probability of extinction of Galton-Watson processes in dynamical environments

针对接近圆上C__一致扩张变换斜积系统的模型，研究其李雅普诺夫指数，提供数值界与计算算法，并应用于动态环境中超临界高尔顿-沃森过程以控制灭绝概率的正则性。

（余）拟不可约与（余）膨胀随机映射

(co)Quasi-irreducible and (co)expanding random maps

本文研究随机$C^1$微分同胚的拟不可约性等性质，建立其等价准则，应用于李雅普诺夫指数连续性与膨胀性，推广形式主义至格拉斯曼丛。