标题： 具有可数分支的预分段凸或扩张映射的系统统计稳定性 显示英文标题

标题： Statistical stability for systems semi-conjugate to pre-piecewise convex or expanding maps with countably many branches

摘要： 我们研究了一类动力系统的统计稳定性，这些系统与具有可数多个分支的预分段凸或扩张映射半共轭。 这些系统可能表现出如无界导数、不连续性或无限马尔可夫划分等复杂特征，这对稳定性分析构成了重大挑战。 考虑到单参数变换族$\{F_\delta\}_{\delta \in [0,1)}$及其对应的不变测度$\{\mu_\delta\}_{\delta \in [0,1)}$，我们提供了确保$\mu_0$统计稳定的条件，即映射$\delta \mapsto \mu_\delta$在适当拓扑下在$\delta = 0$处是连续的。 此外，我们建立了$\mu_\delta$的连续性模量关于扰动参数$\delta$的显式定量估计。 显示英文摘要

摘要： We investigate the statistical stability of a class of dynamical systems that are semi-conjugate to pre-piecewise convex or expanding maps with countably many branches. These systems may exhibit complex features such as unbounded derivatives, discontinuities, or infinite Markov partitions, which pose significant challenges for stability analysis. Considering one-parameter families of transformations $\{F_\delta\}_{\delta \in [0,1)}$ with corresponding invariant measures $\{\mu_\delta\}_{\delta \in [0,1)}$, we provide conditions ensuring that $\mu_0$ is statistically stable, i.e., that the map $\delta \mapsto \mu_\delta$ is continuous at $\delta = 0$ in an appropriate topology. Moreover, we establish explicit quantitative estimates for the modulus of continuity of $\mu_\delta$ in terms of the perturbation parameter $\delta$.