This survey describes the recent advances in the construction of Markov partitions for non-uniformly hyperbolic systems. One important feature of this development comes from a finer theory of non-uniformly hyperbolic systems, which we also describe. The Markov partition defines a symbolic extension that is finite-to-one and onto a non-uniformly hyperbolic locus, and this provides dynamical and statistical consequences such as estimates on the number of closed orbits and properties of equilibrium measures. The class of systems includes diffeomorphisms, flows, and maps with singularities.

中文翻译：

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非均匀双曲系统的符号动力学

本综述描述了为非均匀双曲系统构建马尔可夫分区的最新进展。这一发展的一个重要特征来自非均匀双曲线系统的更精细的理论，我们也对此进行了描述。马尔可夫分区定义了一个有限对一的符号扩展，并且在非均匀双曲轨迹上，这提供了动态和统计结果，例如对闭合轨道数和平衡测量特性的估计。系统类包括微分同胚、流和具有奇点的映射。