Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 031, 9 pages      arXiv:1204.1801      https://doi.org/10.3842/SIGMA.2012.031
Contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”

Superintegrable Stäckel Systems on the Plane: Elliptic and Parabolic Coordinates

Andrey V. Tsiganov
St. Petersburg State University, St. Petersburg, Russia

Received April 10, 2012, in final form May 21, 2012; Published online May 25, 2012

Abstract
Recently we proposed a generic construction of the additional integrals of motion for the Stäckel systems applying addition theorems to the angle variables. In this note we show some trivial examples associated with angle variables for elliptic and parabolic coordinate systems on the plane.

Key words: integrability; superintegrability; separation of variables; Abel equations; addition theorems.

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