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Shadowing property of geodesics in Hedlund's metric

Published online by Cambridge University Press:  17 April 2001

MARK LEVI
MARK LEVI
Affiliation:
Math. Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
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Abstract

In this paper we show that the geodesic flow in a Hedlund-type metric on the 3-torus possesses the shadowing property. This implies, in particular, that any rotation vector is represented by a geodesic, a fact that in the two-dimensional case is given by the Aubry–Mather theory, while in the higher-dimensional case is still unknown.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 1 , February 1997 , pp. 187 - 203
Copyright
1997 Cambridge University Press

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