Discretization and superintegrability all rolled into one

Abstract

Abelian integrals arise in the mathematical description of various physical processes. According to Abel's theorem these integrals are related to motion of a set of points along a plane curve around fixed points, which are relatively little used in physics applications. We propose to interpret coordinates of the fixed points either as parameters of exact discretization or as additional first integrals for equations of motion reduced to Abelian quadratures.

LaTeX with AMS fonts, 13 pages, 2 figures, corrected version

References in corpus (10)

• Simultaneous separation for the Neumann and Chaplygin systems
• Position-dependent mass effects in the electronic transport of two-dimensional quantum systems
• New bi-Hamiltonian systems on the plane
• Backlund transformations and divisor doubling
• Bäcklund transformations for the nonholonomic Veselova system
• Integrable discretization and deformation of the nonholonomic Chaplygin ball
• Elliptic curve arithmetic and superintegrable systems
• Transformation of the Stackel matrices preserving superintegrability
• On exact discretization of the cubic-quintic Duffing oscillator
• On discretization of the Euler top

Cited by in corpus (4)

• Superintegrable systems and Riemann-Roch theorem
• Reduction of divisors and Clebsch system
• Reduction of divisors for classical superintegrable $GL(3)$ magnetic chain
• On two-dimensional Hamiltonian systems with sixth-order integrals of motion