随机标准映射中典型马蹄的丰富性
Abundance of typical horseshoes for the random standard map
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中文总结 AI 辅助
本文提出典型马蹄概念，证明随机标准映射中此类马蹄的丰富性，并建立指数混合与大偏差等统计性质。
中文摘要 AI 辅助
我们引入了一个典型马蹄的概念，它由一对矩形组成，这些矩形在正下密度的时刻允许马尔可夫返回，具有受控的双曲几何，并且其轨道能够阴影典型轨迹。我们证明了随机标准映射中典型马蹄的丰富性，并建立了该系统的若干统计性质，包括指数混合以及相关投影和两点过程的大偏差估计。
英文摘要
We introduce a notion of typical horseshoe, consisting of a pair of rectangles admitting Markov returns at times of positive lower density, with controlled hyperbolic geometry and orbits that shadow typical trajectories. We prove the abundance of typical horseshoes for the random standard map and establish several statistical properties of the system, including exponential mixing and large deviation estimates for the associated projective and two-point processes.
