Geodesic Flow on Hyperbolic Surface — Chaos Spectrum

On compact hyperbolic surfaces (constant negative Gaussian curvature), geodesic flow is an Anosov system — the archetypal uniformly hyperbolic dynamical system. Nearby trajectories diverge exponentially, giving a positive Lyapunov exponent equal to 1 in the unit-curvature case. Visualised here in the Poincaré disk model.

0.80 rad
1.00
300
Est. Lyapunov exponent
λ ≈ —
separation growth rate
Geodesics active
0