标题： 势能的关联数与熵间隙和尖点Hitchin表示 显示英文标题

标题： Correlation Number for Potentials with Entropy Gaps and Cusped Hitchin Representations

摘要： 我们引入了一个相关数，用于在拓扑混合的可数状态马尔可夫移位上具有强熵间隙的两个严格正的、局部霍尔德连续的独立势函数，该马尔可夫移位具有BIP性质。 我们以这种方式为尖点希钦表示对定义了一个相关数。 此外，我们探讨了相关数与曼哈顿曲线之间的联系，以及该相关数的几个刚性性质。 显示英文摘要

摘要： We introduce a correlation number for two strictly positive, locally H\"older continuous, independent potentials with strong entropy gaps at infinity on a topologically mixing countable state Markov shift with BIP. We define in this way a correlation number for pairs of cusped Hitchin representations. Furthermore, we explore the connection between the correlation number and the Manhattan curve, along with several rigidity properties of this correlation number.