English

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.

Keywords

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