Geodesic equivalence and integrability
微分几何
2016-09-07 v1 辛几何
可精确求解与可积系统
solv-int
摘要
We suggest a construction that, given a trajectorial diffeomorphism between two Hamiltonian systems, produces integrals of them. As the main example we treat geodesic equivalence of metrics. We show that the existence of a non-trivially geodesically equivalent metric leads to Liouville integrability, and present explicit formulae for integrals.
引用
@article{arxiv.math/9911062,
title = {Geodesic equivalence and integrability},
author = {Petar J. Topalov and Vladimir S. Matveev},
journal= {arXiv preprint arXiv:math/9911062},
year = {2016}
}
备注
19 pages; LaTeX