慢混合双曲系统中非正则可观测量的统计性质
Statistical properties for irregular observables in slowly mixing hyperbolic systems
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中文总结 AI 辅助
本文针对多项式混合双曲动力系统的非光滑可观测量，证明了相关性衰减等多种统计性质，填补了慢混合双曲系统相关结果的空白，对多学科应用具有重要意义。
中文摘要 AI 辅助
我们针对多项式混合双曲动力系统中具有指示函数形式的非光滑可观测量，证明了多种统计性质，包括相关性衰减、带收敛速率的中心极限定理、极大大偏差及几乎处处不变原理。这类结果此前对于慢混合双曲系统尚不为人知，甚至未被预期成立，尽管它们对物理学及其他科学领域的应用具有重要意义。
英文摘要
We prove various statistical properties (i.e., decay of correlations, central limit theorems with convergence rates, maximal large deviations and almost sure invariance principles) for non-smooth observables in the form of indicators functions in polynomially mixing hyperbolic dynamical systems. Such results were not known (or even expected to hold) for slowly mixing hyperbolic systems, although they are important for applications to physics and other sciences.
