标题： 对应关系的拓扑压变分原理 显示英文标题

标题： Variational principles of topological pressure for correspondences

摘要： 最近，李、李和张引入了对应关系的拓扑压力以及转移概率核的测度熵。 在此基础上，他们建立了满足前向扩张条件的对应关系的变分原理。 在本工作中，我们通过推导两种类型的变分原理扩展了这项研究：(i) 对于一类对应关系，拓扑压力等于不变测度极端点上的测度压力的上确界。 (ii) 对于一般对应关系，无需要求前向扩张性，抽象的变分原理成立。 此外，还研究了对应关系的拓扑压力的可微性和平衡态。 显示英文摘要

摘要： Recently, Li, Li and Zhang introduced the topological pressure for correspondences and measure-theoretic entropy for transition probability kernels. Building thereon, they established a variational principle for correspondences satisfying the forward expansiveness condition. In this work, we extend this research by deriving two types of variational principles: (i) For a class of correspondences, the topological pressure equals the supremum of the measure-theoretic pressures over extreme points of invariant measures. (ii) An abstract variational principle holds for general correspondences without requiring forward expansiveness. Furthermore, the differentiability and equilibrium states of the topological pressure for correspondences are also investigated.