• Corpus ID: 238408089

Superintegrable geodesic flows on the hyperbolic plane

@inproceedings{Valent2021SuperintegrableGF,
  title={Superintegrable geodesic flows on the hyperbolic plane},
  author={Galliano Valent},
  year={2021}
}
In the framework laid down by Matveev and Shevchishin, superintegrability is achieved with one integral linear in the momenta (a Killing vector) and two extra integrals of of any degree above two in the momenta. However these extra integrals may exhibit either a trigonometric dependence in the Killing coordinate (a case we have already solved) or a hyperbolic dependence and this case is solved here. Unfortunately the resulting geodesic flow is never defined on the two-sphere, as was the case… 

On two-dimensional Hamiltonian systems with sixth-order integrals of motion

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0. Introduction.- A. Motivation and History.- B. Organization and Contents.- C. What is New in this Book?.- D. What are the Main Problems Today?.- 1. Basic Facts about the Geodesic Flow.- A.

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