Inversion of a mapping associated with the Aomoto-Forrester system

Abstract

This article is devoted to the study of a general class of Hamiltonian systems which extends the Calogero systems with external quadratic potential associated to any root system. The interest for such a class comes from a previous article of Aomoto and Forrester. We consider first the one-degree of freedom case and compute the Birkhoff series defined near each of its stationary points. In general, the analysis of the system motivates finding some expression for the inverses of a rational map introduced by Aomoto and Forrester. We derive here some diagrammatic expansion series for these inverses.

References in corpus (5)

• Quantum Calogero-Moser Models: Integrability for all Root Systems
• Quadratic Algebra associated with Rational Calogero-Moser Models
• Liouville Integrability of Classical Calogero-Moser Models
• Pendulum Integration and Elliptic Functions
• Rigid motions: action-angles, relative cohomology and polynomials with roots on the unit circle