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Hölder exponents of horocycle foliations on surfaces

Published online by Cambridge University Press:  01 October 1999

MARLIES GERBER  and
VIOREL NIŢICĂ
MARLIES GERBER
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, USA
VIOREL NIŢICĂ
Affiliation:
Institute of Mathematics of the Romanian Academy, P.O. Box 1–764, RO-70700 Bucharest, Romania
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Abstract

We show that the horocycle foliations on a compact $C^{\infty}$ (or even $C^{\omega}$) surface of non-positive curvature can fail to be Lipschitz, even if the curvature vanishes only along a single closed geodesic. We calculate the Hölder exponents of these foliations at vectors tangent to geodesics along which the curvature vanishes.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 5 , October 1999 , pp. 1247 - 1254
Copyright
1999 Cambridge University Press

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