A positive transverse Lyapunov exponent forces new stationary measures off an almost surely invariant manifold, yielding exactly two ergodic stationary measures for weakly damped Lorenz 96.
Arnold, Random dynamical systems, 1st ed.
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Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds
A positive transverse Lyapunov exponent forces new stationary measures off an almost surely invariant manifold, yielding exactly two ergodic stationary measures for weakly damped Lorenz 96.