Ergodic Theory and Dynamical Systems
In this paper we show that any surface in 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.
© 2004 by Cambridge University Press. Available on publisher's site at http://journals.cambridge.org/abstract_S0143385703000269.
Donnay, Victor J., and Charles Pugh. "Finite Horizon Riemann Structures and Ergodicity." Ergodic Theory and Dynamical Systems 24 (2004): 89-106.