The stable norm on the 2-torus at irrational directions
The stable norm on the 2-torus at irrational directions
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 …