On superintegrable systems separable in Cartesian coordinates

Abstract

We continue the study of superintegrable systems of Thompson's type separable in Cartesian coordinates. An additional integral of motion for these systems is the polynomial in momenta of N-th order which is a linear function of angle variables and the polynomial in action variables. Existence of such superintegrable systems is naturally related to the famous Chebyshev theorem on binomial differentials.

8 pages, LaTeX with AMS fonts, with corrected misprints

References in corpus (4)

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Cited by in corpus (9)

• New infinite families of $N$th-order superintegrable systems separating in Cartesian coordinates
• The Kepler problem: polynomial algebra of non-polynomial first integrals
• Transformation of the Stackel matrices preserving superintegrability
• Jacobi last multiplier and two-dimensional superintegrable oscillators
• Doubly Exotic $N$th-order Order Superintegrable Classical Systems Separating in Cartesian Coordinates
• Superintegrable systems with position dependent mass: master symmetry and action-angle methods
• Polynomially Superintegrable Hamiltonians Separating in Cartesian Coordinates
• On two-dimensional Hamiltonian systems with sixth-order integrals of motion
• Superintegrability on the 3-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the Sphere $S^3$ and on the Hyperbolic space $H^3$