arXiv subjects

Guilherme Brandão Guglielmo

Publications and source records attributed to Guilherme Brandão Guglielmo.

2 recordsLinked to original sources

arXiv2026

A Metric Entropy Formula for Magnetic Flows without Conjugate Points

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--Mañé 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.

math.DS↗

arXiv2026

Path Connectivity of Anosov Metrics on Surfaces

We construct a class of Riemannian metrics in closed surfaces of genus greater than one, having Anosov geodesic flows, and some regions of positive curvature, such that for each such surface, there exists a smooth curve of conformal deformations that preserves the Anosov property and connects the surface with a Riemannian metric of negative curvature. The conformal deformation does not arise from geometric flows like the Ricci flow, since it is known that such flows might generate conjugate points in the presence of points of positive curvature in the surface.

math.DS↗