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On maximally superintegrable systems

  • A. V. Tsiganov
Research Articles

Abstract

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.

Key words

superintegrable systems Toda lattices Stackel systems 

MSC2000 numbers

37J35 53B20 

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Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  1. 1.V.A. Fock Institute of PhysicsSt. Petersburg State UniversitySt. PetersburgRussia

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