Rational integrals of 2-dimensional geodesic flows: New examples

Sergei Agapov; Vladislav Shubin

doi:10.1016/j.geomphys.2021.104389

Rational integrals of 2-dimensional geodesic flows: New examples

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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.

Original language	English
Article number	104389
Journal	Journal of Geometry and Physics
Volume	170
DOIs	https://doi.org/10.1016/j.geomphys.2021.104389
Publication status	Published - Dec 2021

Keywords

Bessel functions
Geodesic flow
Rational in momenta first integral

OECD FOS+WOS

1.01 MATHEMATICS
1.03 PHYSICAL SCIENCES AND ASTRONOMY

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10.1016/j.geomphys.2021.104389

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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.",

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author = "Sergei Agapov and Vladislav Shubin",

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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.

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Rational integrals of 2-dimensional geodesic flows: New examples

Abstract

Keywords

OECD FOS+WOS

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