Transformation of the Stackel matrices preserving superintegrability

Abstract

If we take a superintegrable Stackel system and make variables "faster" or "slower", that is equivalent to a trivial transformation of the Stackel matrix and potentials, then we obtain an infinite family of superintegrable systems with explicitly defined additional integrals of motion. We present some examples of such transformations associated with angle variables expressed via logarithmic functions.

15 pages, LaTeX with amsfonts

References in corpus (5)

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• On superintegrable systems separable in Cartesian coordinates
• New bi-Hamiltonian systems on the plane
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Cited by in corpus (4)

• Superintegrable systems and Riemann-Roch theorem
• The Kepler problem: polynomial algebra of non-polynomial first integrals
• Discretization and superintegrability all rolled into one
• Reduction of divisors for classical superintegrable $GL(3)$ magnetic chain