# Royal measures are loosely Kronecker

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A nonhyperbolic ergodic measure is an ergodic invariant measure with one Lyapunov exponent equal zero. Gorodetski, Ilyashenko, Kleptsyn, and Nalsky constructed a nonhyperbolic ergodic measure for a skew product diffeomorphism of the three-dimensional torus. Inspired by this construction, Bonatti, Diaz and Gorodetski gave sufficient condi- tions for weak convergence of a sequence of measures supported on periodic orbits to an ergodic measure. A royal measure is a measure obtained through this scheme.