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 explicit examples of metrics and such integrals are constructed. Few superintegrable systems are found having both a polynomial and a rational integrals which are functionally independent of the Hamiltonian.
|Journal||Journal of Geometry and Physics|
|Publication status||Published - Dec 2021|
- Bessel functions
- Geodesic flow
- Rational in momenta first integral
- 1.01 MATHEMATICS
- 1.03 PHYSICAL SCIENCES AND ASTRONOMY