On the Poincaré half-plane H² with curvature K = −1, geodesics are semicircles orthogonal to the real axis. Geodesic flow on the unit tangent bundle is the archetypal Anosov flow: exponential mixing with Lyapunov exponent λ = 1 (for K = −1).
Separation grows as d(t) = d(0)·e^(√|K|·t) — Anosov mixing