167 citations · 651 across the 16 of their papers we have counts for
17 papers
When a -tensor generates separation of variables of a certain metric
Andrey Yu. Konyaev, Jonathan M. Kress, Vladimir S. Matveev
By a -tensor field , we construct an explicit system of differential invariants that vanish if and only if there (locally) exists a metric for which generates…
Algebraic Conditions for Conformal Superintegrability in Arbitrary Dimension
Jonathan Kress, Konrad Schöbel, Andreas Vollmer
We show that the definition of a second order superintegrable system on a (pseudo-)Riemannian manifold gives rise to a conformally invariant notion of superintegrability. Conformal…
An algebraic geometric classification of superintegrable systems in the Euclidean plane
Jonathan Kress, Konrad Schöbel
We prove that the set of non-degenerate second order maximally superintegrable systems in the complex Euclidean plane carries a natural structure of a projective variety, equipped…
Invariant Classification and Limits of Maximally Superintegrable Systems in 3D
Joshua J. Capel, Jonathan M. Kress, Sarah Post
The invariant classification of superintegrable systems is reviewed and utilized to construct singular limits between the systems. It is shown, by construction, that all superinteg…
Invariant classification of second-order conformally flat superintegrable systems
Joshua Capel, Jonathan Kress
In this paper we continue the work of Kalnins et al in classifying all second-order conformally-superintegrable (Laplace-type) systems over conformally flat spaces, using tools fro…
Extended Kepler-Coulomb quantum superintegrable systems in 3 dimensions
E. G. Kalnins, J. M. Kress, W. Miller
The quantum Kepler-Coulomb system in 3 dimensions is well known to be 2nd order superintegrable, with a symmetry algebra that closes polynomially under commutators. This polynomial…