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Communications in Mathematical Physics

, Volume 233, Issue 1, pp 153–171 | Cite as

Entropy of Quantum Limits

  • Jean Bourgain
  • Elon Lindenstrauss

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.

Keywords

Entropy Manifold Quantum Limit Geodesic Flow Positive Entropy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jean Bourgain
    • 1
  • Elon Lindenstrauss
    • 2
  1. 1.School of Mathematics, Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA. E-mail: bourgain@ias.eduUS
  2. 2.Department of Mathematics, Stanford University, Stanford, CA 94305, USA. E-mail: elonl@math.stanford.eduUS

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