Algebraically linearizable dynamical systems. (English) Zbl 1057.35069

Caseiro, R.; Françoise, J. P.

Albuquerque, Helena (ed.) et al., The J. A. Pereira da Silva birthday schrift on the occasion of his 60th birthday. Coimbra: Universidade de Coimbra, Departamento de Matemática (ISBN 972-8564-35-X/pbk). Textos Mat., Sér. B 32, 35-45 (2002).

A definition of algebraic linearization is introduced in a slightly broader sense. It is proved that the hyperbolic Ruijsenaars-Schneider systems are algebraically linearizable and the perturbations considered by F. Calogero [J. Math. Phys. 38, 5711–5719 (1997; Zbl 0892.58038)] of the hyperbolic Ruijsenaars-Schneider systems which display only periodic orbits of the same period are algebraically linearizable as well.
For the entire collection see [Zbl 0989.00066].

Reviewer: Xianguo Geng (Zhengzhou)

MSC:

35Q58	Other completely integrable PDE (MSC2000)
37J35	Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests

Keywords:

algebraic linearization; hyperbolic Ruijsenaars-Schneider systems; perturbations; periodic orbits