Shadowing property of geodesics in Hedlund's metric

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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.

Original languageEnglish (US)
Pages (from-to)187-203
Number of pages17
JournalErgodic Theory and Dynamical Systems
Volume17
Issue number1
DOIs
StatePublished - Feb 1997

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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