On local description of two-dimensional geodesic flows with a polynomial first integral
URI (for links/citations):http://elib.sfu-kras.ru/handle/2311/32932
Pavlov, M. V.
Царев, С. П.
Journal Name:Journal of Physics A: Mathematical and Theoretical
Journal Quartile in Scopus:Q1
Journal Quartile in Web of Science:Q1
Bibliographic Citation:Pavlov, M. V. On local description of two-dimensional geodesic flows with a polynomial first integral [Текст] / M. V. Pavlov, С. П. Царев // Journal of Physics A: Mathematical and Theoretical: Mathematical and Theoretical. — 2016. — Т. 49 (№ 17). — С. 175201-75221
Текст статьи не публикуется в открытом доступе в соответствии с политикой журнала.
In this paper we present a construction of multiparametric families of two-dimensional metrics with a polynomial first integral of arbitrary degree in momenta. Such integrable geodesic flows are described by solutions of some semi-Hamiltonian hydrodynamic-type system. We give a constructive algorithm for the solution of the derived hydrodynamic-type system, i.e. we found infinitely many conservation laws and commuting flows. Thus we were able to find infinitely many particular solutions of this hydrodynamic-type system by the generalized hodograph method. Therefore infinitely many particular two-dimensional metrics equipped with first integrals polynomial in momenta were constructed.