caa a22 4500 445835974 CHVBK 20180317145330.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00209-010-0662-0 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0662-0 Spiraling spectra of geodesic lines in negatively curved manifolds [Elektronische Daten] [Jouni Parkkonen, Frédéric Paulin] 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. Springer-Verlag, 2010 Geodesic flow nationallicence Negative curvature nationallicence Spiraling nationallicence Dirichlet theorem nationallicence Hall ray nationallicence Diophantine approximation nationallicence Quadratic irrational nationallicence Parkkonen Jouni Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, 40014, University of Jyväskylä, Finland aut Paulin Frédéric Département de Mathématique et Applications, UMR 8553 CNRS, École Normale Supérieure, 45 rue d'Ulm, 75230, Paris Cedex 05, France aut Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 101-142 0025-5874 268:1-2<101 2011 268 209 https://doi.org/10.1007/s00209-010-0662-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0662-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Parkkonen Jouni Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, 40014, University of Jyväskylä, Finland aut NATIONALLICENCE 700 1- Paulin Frédéric Département de Mathématique et Applications, UMR 8553 CNRS, École Normale Supérieure, 45 rue d'Ulm, 75230, Paris Cedex 05, France aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 101-142 0025-5874 268:1-2<101 2011 268 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer