A remark on the phase transition for the geodesic flow of a rank one surface of nonpositive curvature

Keith Burns, Dong Chen

For any rank 1 nonpositively curved surface $M$, it was proved by Burns-Climenhaga-Fisher-Thompson that for any $q<1$, there exists a unique equilibrium state ${\mu }_q$ for $q{\phi }^u$, whe…