Geodesic equivalence and integrability

Petar J. Topalov; Vladimir S. Matveev

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arXiv · math/9911062

Geodesic equivalence and integrability

Petar J. Topalov·Vladimir S. Matveev

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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.

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BibTeX RIS

Petar J. Topalov, Vladimir S. Matveev. 1999-11-10. Geodesic equivalence and integrability. https://arxiv.org/abs/math/9911062

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