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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Dynamics and Zeta functions on conformally compact manifolds
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by Julie Rowlett, Pablo Suárez-Serrato and Samuel Tapie PDF
Trans. Amer. Math. Soc. 367 (2015), 2459-2486 Request permission


In this note, we study the dynamics and associated Zeta functions of conformally compact manifolds with variable negative sectional curvatures. We begin with a discussion of a larger class of manifolds known as convex co-compact manifolds with variable negative curvature. Applying results from dynamics on these spaces, we obtain optimal meromorphic extensions of weighted dynamical Zeta functions and asymptotic counting estimates for the number of weighted closed geodesics. A meromorphic extension of the standard dynamical Zeta function and the prime orbit theorem follow as corollaries. Finally, we investigate interactions between the dynamics and spectral theory of these spaces.
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Additional Information
  • Julie Rowlett
  • Affiliation: Max Planck Institut für Mathematik, Vivatgasse 7, D-53111 Bonn, Germany
  • Email:
  • Pablo Suárez-Serrato
  • Affiliation: Instituto de Matemáticas, Universidad Nacional Autonóma de México, Ciudad Universitaria, Coyoacán, 04510, México, D. F.
  • Email:
  • Samuel Tapie
  • Affiliation: Laboratoire Jean Leray, Université de Nantes, 2, rue de la Houssinière - BP 92208, F-44322 Nantes Cedex 3, France
  • Email:
  • Received by editor(s): June 27, 2011
  • Received by editor(s) in revised form: August 23, 2012
  • Published electronically: November 24, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 2459-2486
  • MSC (2010): Primary 37D40, 58J50, 53C22, 53D25, 35P15
  • DOI:
  • MathSciNet review: 3301870