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Spiraling spectra of geodesic lines in negatively curved manifolds

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An Erratum to this article was published on 19 January 2014

Abstract

Given a negatively curved geodesic metric space M, we study the asymptotic penetration behaviour of geodesic lines of M in small neighbourhoods of closed geodesics and of other compact convex subsets of M. We define a spiraling spectrum which gives precise information on the asymptotic spiraling lengths of geodesic lines around these objects. We prove analogs of the theorems of Dirichlet, Hall and Cusick in this context. As a consequence, we obtain Diophantine approximation results of elements of \({\mathbb{R},\mathbb{C}}\) or the Heisenberg group by quadratic irrational ones.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, 40014, University of Jyväskylä, Finland

    Jouni Parkkonen

  2. Département de Mathématique et Applications, UMR 8553 CNRS, École Normale Supérieure, 45 rue d’Ulm, 75230, Paris Cedex 05, France

    Frédéric Paulin

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  1. Jouni Parkkonen
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  2. Frédéric Paulin
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Correspondence to Frédéric Paulin.

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An erratum to this article is available at http://dx.doi.org/10.1007/s00209-013-1239-5.

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Parkkonen, J., Paulin, F. Spiraling spectra of geodesic lines in negatively curved manifolds. Math. Z. 268, 101–142 (2011). https://doi.org/10.1007/s00209-010-0662-0

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