Erratum for ``Non singular Hamiltonian systems and geodesic flows on surfaces with negative curvature'' (Q1580334)

In this correction to the title paper [ibid. 42, No. 2, 267-299 (1998; Zbl 0997.37026)] the authors show that the new Lagrangian, corresponding to the conformal metric \(g_h\) is equivalent to the classical mechanical Lagrangian, only for the case of one degree of freedom. This implies that Proposition 2 is not valid for two or more degrees of freedom. The remaining part of Section 2 is valid for the geodesic conformal system \((\text{int}(M_h), g_h,U)\). All the results in Section 3 are stated for the original classical mechanical problem. Hence, they are all true, except for the comment about examples in Section 5 on the final line of Section 3. Section 4 refers to the geodesic conformal system \((\text{int}(M_h),g_h,U)\), but not all the results remain valid since it was partly based on Section 3.