Minimal geodesics and topological entropy on T²

2007/07/04 by Eva Leschinsky, Leschinsky, Eva
Mathematics · #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #math.DG #math.DS

paper · pdf · doi:10.48550/arxiv.0707.0673

12 pages

arxiv created 2007/07/04 · arxiv updated 2009/12/01

Abstract

Let (T², g) be a two-dimensional Riemannian torus. In this paper we prove that the topological entropy of the geodesic flow restricted to the set of initial conditions of minimal geodesics vanishes, independent of the choice of the Riemannian metric.

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