An ergodic-averaging method to differentiate covariant Lyapunov vectors

Covariant Lyapunov vectors or CLVs span the expanding and contracting directions of perturbations along trajectories in a chaotic dynamical system. Due to efficient algorithms compute them that only utilize trajectory information, they have been widely applied across scientific disciplines, principally for sensitivity analysis predictions under uncertainty. In this paper, we develop numerical method directional derivatives first CLV its own direction; norm derivative is also curvature one-dimensional unstable manifolds. Similar computation CLVs, present their iterative analogously uses second-order map trajectories, addition Jacobian. We validate new on super-contracting Smale–Williams Solenoid attractor. demonstrate algorithm several other examples including smoothly perturbed Arnold Cat maps, Lorenz’63 attractor, obtaining visualizations each Furthermore, reveal fundamental connection derivation self-derivative with an linear response systems.