An example of a jump from chaos to integrability for magnetic geodesic flows

Details An example of a jump from chaos to integrability for magnetic geodesic flows An example of a jump from chaos to integrability for magnetic geodesic flows

2003-12-23

arxiv.org/abs/math/0312430v2

Math. Notes 76 (2004), 587-589

Mathematics

Dynamical Systems

4 pages

Scientific paper

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

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