Abstract
We study properties of the stable norm on the first homology group of the 2-torus with respect to Riemannian or Finsler metrics, focusing on points with irrational slope. Our results show that the stable norm detects KAM-tori and hyperbolicity in the geodesic flow. Along the way, we shall prove new inequalities for the stable norm near rational directions. Moreover, we study the stable norm in some natural examples reflecting the new results in this paper.
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