313 citations · 679 across the 35 of their papers we have counts for
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The geodesic flow of the BGPP metric is Liouville integrable
Andrzej J. Maciejewski, Maria Przybylska, Galliano Valent
We prove that the geodesics equations corresponding to the BGPP metric are integrable in the Liouville sense. The symmetry of the model allows to reduce…
Koenigs Theorem and Superintegrable Liouville Metrics
Galliano Valent
In a first part, we give a new proof of Koenigs theorem and, in a second part, we determine the local form of all the superintegrable Riemannian Liouville metrics as well as their…
Superintegrable geodesic flows on the hyperbolic plane
Galliano Valent
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 d…
Global structure and geodesics for Koenigs superintegrable systems
Galliano Valent
Starting from the framework defined by Matveev and Shevchishin we derive the local and the global structure for the four types of super-integrable Koenigs metrics. These dynamical…
Zoll and Tannery metrics from a superintegrable geodesic flow
Galliano Valent
We prove that for Matveev and Shevchishin superintegrable system, with a linear and a cubic integral, the metrics defined on S^2 and on Tannery's orbifold T^2 are either Zoll or Ta…
Explicit metrics for a class of two-dimensional superintegrable systems
Galliano Valent, Christian Duval, Vsevolod Shevchishin
We obtain, in local coordinates, the explicit form of the two-dimensional, super-integrable systems of Matveev and Shevchishin involving cubic integrals. This enables us to determi…