Rational integrals of 2-dimensional geodesic flows: new examples
Dynamical Systems
2021-10-27 v1 Analysis of PDEs
Differential Geometry
Abstract
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.
Cite
@article{arxiv.2106.10645,
title = {Rational integrals of 2-dimensional geodesic flows: new examples},
author = {Sergei Agapov and Vladislav Shubin},
journal= {arXiv preprint arXiv:2106.10645},
year = {2021}
}