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Caseiro, Raquel; Francoise, Jean-Pierre; Sasaki, Ryu

Inversion of a mapping associated with the Aomoto-Forrester system. (English) Zbl 1348.37088

Rev. Math. Phys. 25, No. 10, Article ID 1343009, 10 p. (2013).
Summary: 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 K. Aomoto and P. J. Forrester [Compos. Math. 121, No. 3, 263–295 (2000; Zbl 0967.32025)]. 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 [loc. cit.]. We derive here some diagrammatic expansion series for these inverses.

Cited in 1 Review

MSC:

37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
37J30 Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria)
70H20 Hamilton-Jacobi equations in mechanics

Keywords:

Birkhoff normal form; arrangement of hyperplanes; Hamilton-Jacobi equation; diagrammatic expansions

Citations:

Zbl 0967.32025
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Full Text: DOI arXiv

References:

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