In the pioneering work by Dimitrov–Haiden–Katzarkov–Kontsevich, they introduced various categorical analogies from the classical theory of dynamical systems. In particular, they defined the entropy of an endofunctor on a triangulated category with a split generator. In the connection between the categorical theory and the classical theory, a stability condition on a triangulated category plays the role of a measured foliation so that one can measure the “volume” of objects, called the mass, via the stability condition. The aim of this paper is to establish fundamental properties of the growth rate of mass of objects under the mapping by the endofunctor and to clarify the relationship between it and the entropy. We also show that they coincide under a certain condition.

中文翻译：

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对象的大规模增长和类别熵

在 Dimitrov-Haiden-Katzarkov-Kontsevich 的开创性工作中，他们引入了来自经典动力系统理论的各种分类类比。特别是，他们用分裂生成器定义了三角分类上的内函子的熵。在范畴论和经典理论之间的联系中，三角范畴的稳定性条件起到了测量叶状结构的作用，因此人们可以通过稳定性条件来测量物体的“体积”，称为质量。本文的目的是建立内函子映射下物体质量增长率的基本性质，并阐明它与熵之间的关系。我们还表明它们在一定条件下是一致的。