We study the one parameter family of potential functions $q{\phi }^u$ associated with the unstable Jacobian potential (or geometric potential) ${\phi }^u$ for the geodesic flow of a compact rank 1 surface of nonpositive curvature. For q<1, it is known that there is a unique equilibrium state associated with $q{\phi }^u$, and it has full support. For q>1 it is known that an invariant measure is an equilibrium state if and only if it is supported on the singular set. We study the critical value q = 1 and show that the ergodic equilibrium states are either the restriction to the regular set of the Liouville measure or measures supported on the singular set. In particular, when q = 1, there is a unique ergodic equilibrium state that gives positive measure to the regular set.

我们研究势函数的单参数族 $q{\phi }^{你}$ 与不稳定的雅可比势（或几何势）相关联 ${\phi }^{你}$用于非正曲率的紧凑秩 1 表面的测地线流动。对于q <1，已知有一个独特的平衡状态与$q{\phi }^{你}$，并得到全力支持。对于q >1，已知不变测度是均衡状态当且仅当它在奇异集上得到支持。我们研究了临界值q  = 1 并表明遍历平衡状态要么是对 Liouville 测度的正则集的限制，要么是在奇异集上支持的测度。特别是，当 q  = 1 时，存在一个独特的遍历平衡状态，它对正则集给出了正测度。