Explore Lyapunov exponents for small random perturbations in a one-hour seminar from the Symplectic Dynamics/Geometry series. Delve into the study of predominantly hyperbolic two-dimensional volume-preserving diffeomorphisms, including the Standard Map. Learn about hyperbola city, asymptotic dynamical regimes, one-dimensional examples, invariant cones, and elliptic islands. Examine Gorodetsky's results on random perturbations, stationary measures, and the interplay between stationarity and dynamics. Gain insights from speaker Alex Blumenthal of the University of Maryland as he presents at the Institute for Advanced Study.