A generic property of families of Lagrangian systems

TL;DR

This paper proves that for a broad class of Lagrangian systems, typically, there are only finitely many measures that minimize the action for each cohomology class, highlighting a universal property.

Contribution

It establishes a generic property of Lagrangian systems, showing finiteness of minimizing measures across all cohomology classes, which was previously unknown.

Findings

Finitely many minimizing measures for generic Lagrangians

Universal property across cohomology classes

Advances understanding of Lagrangian dynamics

Abstract

We prove that a generic lagrangian has finitely many minimizing measures for every cohomology class.