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Sharp polynomial bounds on the number of Pollicott–Ruelle resonances

Published online by Cambridge University Press:  11 March 2013

KIRIL DATCHEV ,
SEMYON DYATLOV  and
MACIEJ ZWORSKI
KIRIL DATCHEV
Affiliation:
Department of Mathematics, 77 Massachusetts Avenue, Massachusetts Institute of Technology, Cambridge, MA 02139, USA email datchev@math.mit.edu
SEMYON DYATLOV
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA email dyatlov@math.berkeley.eduzworski@math.berkeley.edu
MACIEJ ZWORSKI
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA email dyatlov@math.berkeley.eduzworski@math.berkeley.edu
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Abstract

We give a sharp polynomial bound on the number of Pollicott–Ruelle resonances. These resonances, which are complex numbers in the lower half-plane, appear in expansions of correlations for Anosov contact flows. The bounds follow the tradition of upper bounds on the number of scattering resonances and improve a recent bound of Faure and Sjöstrand. The complex scaling method used in scattering theory is replaced by an approach using exponentially weighted spaces introduced by Helffer and Sjöstrand in scattering theory and by Faure and Sjöstrand in the theory of Anosov flows.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 4 , August 2014 , pp. 1168 - 1183
Copyright
Copyright ©2013 Cambridge University Press 

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