C\({}^ k\)-rigidity for hyperbolic flows. II (Q916186)

[For part I see ibid. 61, No.1, 14-28 (1988; Zbl 0673.58032).] The following interesting results are proved. Any conjugating homeomorphism between two geodesic flows for compact surfaces of negative curvature is necessarily \({\mathcal C}^{\infty}\). For any two measurably isomorphic horocycle flows, the conjugating map must have a \({\mathcal C}^{\infty}\) version. As the author indicates, similar results are independently obtained by J. Marco.