Surfaces with nonpositive magnetic curvature

Abstract

For a negatively curved surface, magnetic (or twisted geodesic) flows with nonpositive ''magnetic curvature'' have a large-scale geometry on the universal cover that retains some features associated with geodesic flows: magnetic boundary and visibility, possibly magnetically flat strips. This has dynamical consequences: orbit-equivalence to the geodesic flow, density of periodic points, transitivity, entropy-expansivity, existence of equilibrium states.

59 pages, 12 figures