JMD
Remarks on quantum ergodicity
Gabriel Rivière
Journal of Modern Dynamics 2013, 7(1): 119-133 doi: 10.3934/jmd.2013.7.119
We prove a generalized version of the Quantum Ergodicity Theorem on smooth compact Riemannian manifolds without boundary. We apply it to prove some asymptotic properties on the distribution of typical eigenfunctions of the Laplacian in geometric situations in which the Liouville measure is not (or not known to be) ergodic.
keywords: Eigenfunctions of the Laplacian quantum ergodicity nonuniformly hyperbolic dynamical systems.

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