Shadowing property of geodesics in Hedlund's metric

Mark Levi

doi:10.1017/S0143385797060999

Shadowing property of geodesics in Hedlund's metric

Mark Levi

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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 language	English (US)
Pages (from-to)	187-203
Number of pages	17
Journal	Ergodic Theory and Dynamical Systems
Volume	17
Issue number	1
DOIs	https://doi.org/10.1017/S0143385797060999
State	Published - Feb 1997

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1017/S0143385797060999

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title = "Shadowing property of geodesics in Hedlund's metric",

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.",

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AB - 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.

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JO - Ergodic Theory and Dynamical Systems

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Shadowing property of geodesics in Hedlund's metric

Abstract

All Science Journal Classification (ASJC) codes

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