Research of Artur Sergyeyev on Dynamical Systems

In the paper

Exact solvability of superintegrable Benenti systems (arXiv version)

we established quantum and classical exact solvability for two large classes of maximally superintegrable Benenti systems in n dimensions with arbitrarily large natural n

(For the background on superintegrability see here if necessary).

See also the related paper with Maciej Błaszak, Ziemowit Domański and Błażej M. Szablikowski

Integrable quantum Stäckel systems (arXiv version)

and the paper with Pavel Krtouš on quantum integrability for the Klein-Gordon equation on a class of curved backgrounds

Complete set of commuting symmetry operators for the Klein-Gordon equation in generalized higher-dimensional Kerr-NUT-(A)dS spacetimes

See also my paper

Coupling constant metamorphosis as an integrability-preserving transformation for general finite-dimensional dynamical systems and ODEs (arXiv version)

where the multiparameter coupling constant metamorphosis, also known as the generalized Stäckel transform, is extended to general (not necessarily Hamiltonian) dynamical systems,

and the papers with Maciej Błaszak on integrable and superintegrable Hamiltonian systems

Maximal superintegrability of Benenti systems (arXiv version)

Natural coordinates for a class of Benenti systems (arXiv version)

Generalized Stäckel transform and reciprocal transformations for finite-dimensional integrable systems (arXiv version)

Generalized Stäckel systems


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