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Finite horizon Riemann structures and ergodicity

Published online by Cambridge University Press:  02 February 2004

VICTOR J. DONNAY and
CHARLES PUGH
VICTOR J. DONNAY
Affiliation:
Mathematics Department, Bryn Mawr, PA 19010, USA (e-mail: vdonnay@brynmawr.edu)
CHARLES PUGH
Affiliation:
Mathematics Department, University of California, Berkeley, CA 94720, USA (e-mail: pugh@math.berkeley.edu)
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Abstract

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In this paper we show that any surface in $\mathbb{R}^3$ can be modified by gluing on small ‘focusing caps’ so that its geodesic flow becomes ergodic. A new concept, finite horizon cap geometry, is what makes the construction work.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 1 , February 2004, pp. 89 - 106
Copyright
2004 Cambridge University Press