Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Bocher contractions of conformally superintegrable Laplace equations: Detailed computations

E. G. Kalnins, W. Miller, E. Subag

Abstract

These supplementary notes in the ArXiv are a companion to our paper "Bocher contractions of conformally superintegrable Laplace equations" [arXiv:1512.09315]. They contain background material and the details of the extensive computations that couldn't be put in the paper, due to space limitations.

Bocher contractions of conformally superintegrable Laplace equations: Detailed computations

Abstract

These supplementary notes in the ArXiv are a companion to our paper "Bocher contractions of conformally superintegrable Laplace equations" [arXiv:1512.09315]. They contain background material and the details of the extensive computations that couldn't be put in the paper, due to space limitations.

Paper Structure

This paper contains 72 sections, 4 theorems, 319 equations.

Table of Contents

  1. 2D conformal superintegrability of the 2nd order
  2. The integrability conditions for the potential
  3. The conformal Stäckel transform
  4. Contractions of conformal superintegrable systems with potential induced by generalized Inönü-Wigner contractions
  5. Tetraspherical coordinates and relations with the 2-sphere and 2D flat space
  6. Classification of 2nd order conformally superintegrable systems with nondegenerate potential
  7. Relation to separation of variables
  8. Bôcher contractions
  9. The $[1,1,1,1]$ to $[2,1,1]$ contraction
  10. Conformal Stäckel transforms of the [1,1,1,1] system
  11. [1,1,1,1] to [2,1,1] contraction and Stäckel transforms
  12. Conformal Stäckel transforms of the [2,1,1] system
  13. Conformal Stäckel transforms of the [0] system
  14. [1,1,1,1] to [2,2]:
  15. Conformal Stäckel transforms of the [2,2] system
  16. ...and 57 more sections

Key Result

Theorem \oldthetheorem

The transformed (Helmholtz) system (helms) is truly superintegrable.

Theorems & Definitions (6)

  • Theorem \oldthetheorem
  • Corollary 1
  • Theorem \oldthetheorem
  • Theorem \oldthetheorem
  • Example 1
  • Example 2