Helicity and the Ma\~n\'e critical value

TL;DR

This paper explores the connection between magnetic flow helicity and the Mañé critical value on closed surfaces of genus at least 2, revealing a fundamental relationship in dynamical systems and geometric analysis.

Contribution

It establishes a novel link between helicity and the Mañé critical value for magnetic flows on higher genus surfaces, advancing understanding in geometric dynamics.

Findings

Identifies a direct relationship between helicity and the Mañé critical value.

Provides new insights into magnetic flows on surfaces of genus ≥ 2.

Enhances theoretical framework connecting topology and dynamical invariants.

Abstract

We establish a relationship between the helicity of a magnetic flow on a closed surface of genus $\geq 2$ and the Ma\~n\'e critical value.