TY - JOUR

T1 - On maximally superintegrable systems

AU - Tsiganov, A. V.

PY - 2008/6/1

Y1 - 2008/6/1

N2 - Locally any completely integrable system is maximally superintegrable system since we have the necessary number of the action-angle variables. The main problem is the construction of the single-valued additional integrals of motion on the whole phase space by using these multi-valued action-angle variables. Some constructions of the additional integrals of motion for the Stäckel systems and for the integrable systems related with two different quadratic r-matrix algebras are discussed. Among these system there are the open Heisenberg magnet and the open Toda lattices associated with the different root systems.

AB - Locally any completely integrable system is maximally superintegrable system since we have the necessary number of the action-angle variables. The main problem is the construction of the single-valued additional integrals of motion on the whole phase space by using these multi-valued action-angle variables. Some constructions of the additional integrals of motion for the Stäckel systems and for the integrable systems related with two different quadratic r-matrix algebras are discussed. Among these system there are the open Heisenberg magnet and the open Toda lattices associated with the different root systems.

KW - Stackel systems

KW - Superintegrable systems

KW - Toda lattices

UR - http://www.scopus.com/inward/record.url?scp=45549087558&partnerID=8YFLogxK

U2 - 10.1134/S1560354708030040

DO - 10.1134/S1560354708030040

M3 - Article

AN - SCOPUS:45549087558

VL - 13

SP - 178

EP - 190

JO - Regular and Chaotic Dynamics

JF - Regular and Chaotic Dynamics

SN - 1560-3547

IS - 3

ER -