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

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. T...

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Veröffentlicht in:	arXiv.org 2015-09
Hauptverfasser:	Pavlov, Maxim V, Tsarev, Sergey P
Format:	Artikel
Sprache:	eng
Schlagworte:	Conservation laws Integrals Mathematics - Differential Geometry Mathematics - Dynamical Systems Mathematics - Mathematical Physics Physics - Exactly Solvable and Integrable Systems Physics - Mathematical Physics Polynomials Two dimensional flow
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