The stable norm on the 2-torus at irrational directions
Stefan Klempnauer, Jan Philipp Schr\"oder
TL;DR
This paper investigates the stable norm on the 2-torus for irrational directions, revealing its ability to detect KAM-tori and hyperbolic structures in geodesic flows, with analysis of natural examples.
Contribution
It demonstrates how the stable norm characterizes complex dynamical features like KAM-tori and hyperbolicity for irrational directions on the 2-torus.
Findings
Stable norm detects KAM-tori in geodesic flow.
Stable norm identifies hyperbolic structures.
Analysis of natural examples of Finsler metrics.
Abstract
We study the structure of the stable norm of Finsler metrics on the 2-torus with a focus to points of irrational slope. By our results, the stable norm detects KAM-tori and hyperbolicity in the geodesic flow. Moreover, we study the stable norm in some natural examples.
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