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Please note special location. ÌýIf (M,g) is a compact real analytic Riemannian manifold, we give a necessary and sufficient condition for there to be a sequence of quasimodes saturating sup-norm estimates. ÌýThe condition is that there exists a self-focal point x_0\in M for the geodesic flow at which the associated Perron-Frobenius operator U: L^2(S_{x_0}^*M) \to L^2(S_{x_0}^*M) has a nontrivial invariant function. ÌýThe proof is based on von Neumann's ergodic theorem and stationary phase. ÌýIn two dimensions, the condition simplifies and is equivalent to the condition that there be a point through which the geodesic flow is periodic. ÌýThis is joint work with Steve Zelditch.Ìý