On local description of two-dimensional geodesic flows with a polynomial first integral

Описание

Тип публикации: статья из журнала

Год издания: 2016

Идентификатор DOI: 10.1088/1751-8113/49/17/175201

Ключевые слова: geodesic flows, integrability, generalized hodograph method, 37J35, 37K05, 37K10, 70H05, generalized hodograph method Mathematics Subject Classification: 53D25

Аннотация: 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 derivedПоказать полностьюhydrodynamic-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.

Ссылки на полный текст

Издание

Журнал: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

Выпуск журнала: Vol. 49, Is. 17

ISSN журнала: 17518113

Место издания: BRISTOL

Издатель: IOP PUBLISHING LTD

Персоны

  • Pavlov M.V. (Department of Mechanics and Mathematics,Novosibirsk State University)
  • Tsarev S.P. (Siberian Federal University,Institute of Space and Information Technologies)