TY - JOUR

T1 - New examples of non-polynomial integrals of two-dimensional geodesic flows

AU - Agapov, Sergei

AU - Shubin, Vladislav

N1 - The first author is supported by the Mathematical Center in Akademgorodok under the Agreement No. 075-15-2022-282 with the Ministry of Science and Higher Education of the Russian Federation.

PY - 2024/1/5

Y1 - 2024/1/5

N2 - In this paper, we continue to study integrable geodesic flows on 2-surfaces with non-polynomial first integrals which we started earlier in our previous papers. We construct explicitly new local examples of Riemannian metrics and such integrals via various approaches and methods such as the classical and the generalized hodograph methods, the method of separation of variables and some others.

AB - In this paper, we continue to study integrable geodesic flows on 2-surfaces with non-polynomial first integrals which we started earlier in our previous papers. We construct explicitly new local examples of Riemannian metrics and such integrals via various approaches and methods such as the classical and the generalized hodograph methods, the method of separation of variables and some others.

KW - associated Legendre functions

KW - generalized hodograph method

KW - integrable geodesic flow

KW - non-polynomial first integral

KW - semi-Hamiltonian system

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85180086222&origin=inward&txGid=ed2c68a7e224c7617bddaaedee82c6eb

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:001118878000001

UR - https://www.mendeley.com/catalogue/7a34ab58-d70d-30b1-a7e6-5034a5a52db5/

U2 - 10.1088/1751-8121/ad0fb3

DO - 10.1088/1751-8121/ad0fb3

M3 - Article

VL - 57

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 1

M1 - 015204

ER -