2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69691It is proved that the motion of a charge particle on a hyperbolic oriented two-dimensional surface in a magnetic field given by the volume form of the hyperbolic metric is completely integrable on the energy levels E < 1/2 in terms of real-analytic integrals. However it was known that on the level E=1/2 every trajectory is transitive and the restrictions of this flow onto the levels E>1/2 are Anosov flows4 pagesDynamical SystemsMathematical PhysicsChaotic Dynamicstext