TY - JOUR

T1 - Rational integrals of 2-dimensional geodesic flows: New examples

AU - Agapov, Sergei

AU - Shubin, Vladislav

N1 - Funding Information: Both authors are supported by the Mathematical Center in Akademgorodok under the agreement No. 075-15-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation . Publisher Copyright: © 2021 Elsevier B.V.

PY - 2021/12

Y1 - 2021/12

N2 - 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.

AB - 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.

KW - Bessel functions

KW - Geodesic flow

KW - Rational in momenta first integral

UR - http://www.scopus.com/inward/record.url?scp=85116478201&partnerID=8YFLogxK

U2 - 10.1016/j.geomphys.2021.104389

DO - 10.1016/j.geomphys.2021.104389

M3 - Article

AN - SCOPUS:85116478201

VL - 170

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

M1 - 104389

ER -