Leonard Euler: addition theorems and superintegrable systems

Abstract

We consider the Euler approach to construction and to investigation of the superintegrable systems related to the addition theorems. As an example we reconstruct Drach systems and get some new two-dimensional superintegrable Stackel systems.

The text of the talk at International Conference Geometry, Dynamics, Integrable Systems, September 2-7, 2008, Belgrade, Serbia, LaTeX, 18 pages

References in corpus (5)

• Superintegrable Systems with a Third Order Integrals of Motion
• Nondegenerate 3D complex Euclidean superintegrable systems and algebraic varieties
• On maximally superintegrable systems
• Symbolic software for separation of variables in the Hamilton-Jacobi equation for the L-systems
• Addition theorems and the Drach superintegrable systems

Cited by in corpus (15)

• On algebraic construction of certain integrable and super-integrable systems
• On superintegrable systems separable in Cartesian coordinates
• Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials
• First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator
• Structure Theory for Extended Kepler-Coulomb 3D Classical Superintegrable Systems
• Elliptic curve arithmetic and superintegrable systems
• Superintegrable systems and Riemann-Roch theorem
• The Kepler problem: polynomial algebra of non-polynomial first integrals
• Transformation of the Stackel matrices preserving superintegrability
• On the superintegrable Richelot systems
• Discretization and superintegrability all rolled into one
• Superintegrable Stäckel Systems on the Plane: Elliptic and Parabolic Coordinates
• Projectively equivalent 2-dimensional superintegrable systems with projective symmetries
• Jacobi last multiplier and two-dimensional superintegrable oscillators
• Addition theorems for Ck real functions and applications in ordinary differential equations