2003/12/31 by I. A. Taimanov
Mathematics · Physics and Astronomy · #math.DS #math-ph #math.MP #nlin.CD
published as Math. Notes 76 (2004), 587-589 · 4 pages
arxiv created 2005/03/01 · arxiv updated 2009/12/01
It 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 flows