Addition theorems and the Drach superintegrable systems

Abstract

We propose new construction of the polynomial integrals of motion related to the addition theorems. As an example we reconstruct Drach systems and get some new two-dimensional superintegrable Stackel systems with third, fifth and seventh order integrals of motion.

18 pages, the talk given on the conference "Superintegrable Systems in Classical and Quantum Mechanics", Prague 2008

References in corpus (3)

• Polynomial Poisson Algebras for Classical Superintegrable Systems with a Third Order Integral of Motion
• On maximally superintegrable systems
• Symbolic software for separation of variables in the Hamilton-Jacobi equation for the L-systems

Cited by in corpus (8)

• On algebraic construction of certain integrable and super-integrable systems
• Leonard Euler: addition theorems and superintegrable systems
• On superintegrable systems separable in Cartesian coordinates
• Superintegrable systems and Riemann-Roch theorem
• Transformation of the Stackel matrices preserving superintegrability
• On the superintegrable Richelot systems
• Higher order first integrals of autonomous dynamical systems
• Jacobi last multiplier and two-dimensional superintegrable oscillators