Abstract:
In this paper we show that any measure arising as a weak* limit of microlocal lifts of eigenfunctions of the Laplacian on certain arithmetic manifolds have dimension at least 11/9, and in particular all ergodic components of this measure with respect to the geodesic flow have positive entropy.
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Received: 14 March 2002 / Accepted: 24 June 2002 Published online: 13 January 2003
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Bourgain, J., Lindenstrauss, E. Entropy of Quantum Limits. Commun. Math. Phys. 233, 153–171 (2003). https://doi.org/10.1007/s00220-002-0770-8
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DOI: https://doi.org/10.1007/s00220-002-0770-8