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arXiv · 2606.18434

A Metric Entropy Formula for Magnetic Flows without Conjugate Points

Guilherme Brandão Guglielmo·Anthony J. García
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Abstract

In this paper, we use the recently introduced notation and terminology for magnetic systems, which provide a natural framework for extending techniques and results from the theory of geodesic flows to magnetic flows. In this context, we prove a magnetic analogue of the classical Freire--Ma\~n\'e theorem and obtain some applications. As a consequence, we show that for an energy level of a magnetic system without focal points, either the metric entropy is positive or the magnetic curvature is identically zero.

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Guilherme Brandão Guglielmo, Anthony J. García. 2026-06-16. A Metric Entropy Formula for Magnetic Flows without Conjugate Points. https://arxiv.org/abs/2606.18434

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