On Local Description of Two-Dimensional Geodesic Flows with a Polynomial First Integral

Abstract

In this paper we construct multiparametric families of two dimensional metrics with polynomial first integral. Such integrable geodesic flows are described by solutions of some semi-Hamiltonian hydrodynamic type system. We find infinitely many conservation laws and commuting flows for this system. This procedure allows us to present infinitely many particular metrics by the generalized hodograph method.

21 pages

References in corpus (1)

• Classification of integrable hydrodynamic chains and generating functions of conservation laws

Cited by in corpus (2)

• Hydrodynamic-type systems describing 2-dimensional polynomially integrable geodesic flows
• Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method