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We exhibit scarring for certain nonlinear ergodic toral automorphisms. Thereare perturbed quantized hyperbolic toral automorphisms preserving certainco-isotropic submanifolds. The classical dynamics is ergodic, hence in thesemiclassical limit almost all eigenstates converge to the volume measure ofthe torus. Nevertheless, we show that for each of the invariant submanifolds,there are also eigenstates which localize and converge to the volume measure ofthe corresponding submanifold.Comment: 17 page

Scarring on Invariant Manifolds for Perturbed Quantized Hyperbolic Toral Automorphisms