Generic properties of magnetic flows

TL;DR

This paper extends fundamental theorems like Kupka-Smale and Franks lemma to magnetic flows on manifolds of any dimension, using geometric control theory, thereby generalizing previous surface-specific results.

Contribution

It introduces a new approach based on geometric control theory to prove key dynamical properties of magnetic flows in higher dimensions.

Findings

Kupka-Smale theorem established for magnetic flows in any dimension

Franks lemma proved for magnetic flows in any dimension

Method relies on geometric control theory, generalizing previous surface results

Abstract

We obtain Kupka-Smale theorem and Franks lemma for magnetic flows on manifolds with any dimension. This improves Miranda result on surfaces. However our methods relies on geometric control theory, like in Rifford and Ruggiero articles.