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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Invariant relations for the Bowen-Series transform
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by Vincent Pit
Conform. Geom. Dyn. 16 (2012), 103-123
Published electronically: April 16, 2012


Consider the Bowen-Series transform $T$ associated with an even corners fundamental domain of finite volume for some Fuchsian group $\Gamma$. We prove a generic invariance result that abstracts Series’ orbit-equivalence theorem to families of relations on the unit circle. Two applications of this result are developed. We first prove that $T$ satisfies a strong-orbit equivalence property, which allows to identify its hyperbolic periodic orbits with primitive hyperbolic conjugacy classes of $\Gamma$. Then, we show thanks to the invariance theorem that the eigendistributions for the eigenvalue $1$ of the transfer operator of $T$ with spectral parameter $s \in \mathbb {C}$ are in bijection with smooth bounded eigenfunctions for the eigenvalue $s(1-s)$ of the hyperbolic Laplacian on the quotient $\mathbb {D} / \Gamma$.
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Bibliographic Information
  • Vincent Pit
  • Affiliation: Département de Mathématiques d’Orsay, Université Paris-Sud 11, 91405 Orsay Cedex, France
  • Email:
  • Received by editor(s): December 7, 2011
  • Published electronically: April 16, 2012
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 16 (2012), 103-123
  • MSC (2010): Primary 37D40; Secondary 37C30, 58C40
  • DOI:
  • MathSciNet review: 2910743