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Title:  On integrability of magnetic geodesic flows on 2-torus on all energy levels
 
Abstract: 

The questions related to integrability of geodesic flows and magnetic geodesic flows on a 2-torus are considered. 
It is proved for magnetic geodesic flow there is no irreducible polynomial in momenta first integrals of degree 3, 4 or 5 on all energy levels. 


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