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A Local Trace Formula for Anosov Flows

Annales Henri Poincaré volume 18, pages 1–35 (2017)Cite this article

Abstract

We prove a local trace formula for Anosov flows. It relates Pollicott–Ruelle resonances to the periods of closed orbits. As an application, we show that the counting function for resonances in a sufficiently wide strip cannot have a sublinear growth. In particular, for any Anosov flow there exist strips with infinitely many resonances.

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Authors and Affiliations

  1. CMSA, Harvard University, Cambridge, MA, 02138, USA

    Long Jin

  2. Department of Mathematics, University of California, Berkeley, CA, 94720, USA

    Maciej Zworski

Authors
  1. Long Jin
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  2. Maciej Zworski
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Corresponding author

Correspondence to Long Jin.

Additional information

Communicated by Dmitry Dolgopyat.

With appendices by Frédéric Naud

Frédéric Naud address is Laboratoire d'Analyse nonlinéaire et géométrie, Université d'Avignon, Avignon, France and his email address is frederic.naud@univ-avignon.fr.

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Jin, L., Zworski, M. A Local Trace Formula for Anosov Flows. Ann. Henri Poincaré 18, 1–35 (2017). https://doi.org/10.1007/s00023-016-0504-7

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  • DOI: https://doi.org/10.1007/s00023-016-0504-7

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