Geodesic equivalence and integrability
Differential Geometry
2016-09-07 v1 Symplectic Geometry
Exactly Solvable and Integrable Systems
solv-int
Abstract
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.
Cite
@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}
}
Comments
19 pages; LaTeX