Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method

Autor:	Agapov, Sergei
Rok vydání:	2024
Předmět:	Mathematics - Dynamical Systems Mathematics - Analysis of PDEs Mathematics - Differential Geometry 37J35 53D25 70H06 35C05
Druh dokumentu:	Working Paper
Popis:	We study Riemannian metrics on 2-surfaces with integrable geodesic flows such that an additional first integral is high-degree polynomial in momenta. This problem reduces to searching for solutions to certain quasi-linear systems of PDEs which turn out to be semi-Hamiltonian. We construct plenty of local explicit and implicit integrable examples with polynomial first integrals of degrees 3, 4, 5. Our construction is essentially based on applying the generalized hodograph method.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.18920 Zobrazit plný text záznamu View this record from Arxiv