The $C^0$ integrability of symplectic twist maps without conjugate points

TL;DR

This paper proves that symplectic twist maps on the cotangent bundle of a torus without conjugate points are continuously foliated by invariant Lagrangian graphs, establishing their $C^0$ integrability.

Contribution

It demonstrates the $C^0$ integrability of symplectic twist maps without conjugate points, a significant extension of integrability theory in symplectic dynamics.

Findings

Symplectic twist maps without conjugate points are $C^0$ integrable.

The cotangent bundle admits a continuous foliation by invariant Lagrangian graphs.

Abstract

We prove that symplectic twist maps defined on the cotangent bundle of the d-dimensional torus that have no conjugate points are $C^0$ integrable, i.e. the cotangent bundle is continuously foliated by a family of invariant Lagrangian graphs.