Ergodic Theory and Dynamical Systems



Geodesics avoiding open subsets in surfaces of negative curvature


SERGEI BUYALO a1, VIKTOR SCHROEDER a2 and MICHEL WALZ a2
a1 St. Petersburg Branch, V. A. Steklov Institute of Mathematics (POMI), Russian Academy of Sciences, Fontanka 27, St. Petersburg, 191011, Russia (e-mail: buyalo@pdmi.ras.ru)
a2 Mathematisches Institut, Universität Zürich, Winterthurer Str. 190, CH-8057 Zürich, Switzerland (e-mail: {vschroed,mwalz}@math.unizh.ch)

Abstract

We prove existence and non-existence results for geodesics avoiding $a$-separated sets on a surface of negative curvature.

(Received June 11 1998)
(Revised June 9 1999)