The stable norm on the 2-torus at irrational directions

被引：1

作者：

Klempnauer, Stefan ^{[1
]}

Schroder, Jan Philipp ^{[1
]}

机构：

[1] Ruhr Univ, Fac Math, D-44780 Bochum, Germany

来源：

NONLINEARITY | 2017年 / 30卷 / 03期

关键词：

Finsler metric; stable norm; Mather's action functional; minimal geodesic; KAM-torus; hyperbolicity; AUBRY-MATHER SETS; MINIMIZING MEASURES; GEODESICS; CURVES;

D O I：

10.1088/1361-6544/aa5520

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：912 / 942

页数：31