3 citations · 4 across the 3 of their papers we have counts for
4 papers
Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method
Sergei Agapov
We study Riemannian metrics on 2-surfaces with integrable geodesic flows such that an additional first integral is high-degree polynomial in momenta. This problem reduces to search…
Integrable magnetic geodesic flows on 2-surfaces
Sergei Agapov, Alexey Potashnikov, Vladislav Shubin
We study the magnetic geodesic flows on 2-surfaces having an additional first integral which is independent of the Hamiltonian at a fixed energy level. The following two cases are…
Rational integrals of 2-dimensional geodesic flows: new examples
Sergei Agapov, Vladislav Shubin
This paper is devoted to searching for Riemannian metrics on 2-surfaces whose geodesic flows admit a rational in momenta first integral with a linear numerator and denominator. The…
Integrable magnetic geodesic flows on 2-torus: new example via quasi-linear system of PDEs
Sergey V. Agapov, Michael, Bialy +1
The only one example has been known of magnetic geodesic flow on the 2-torus which has a polynomial in momenta integral independent of the Hamiltonian. In this example the integral…