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Integrable discretizations of the Euler top

By A.I. Bobenko, B. Lorbeer, Yu.B. (Berlin Technische Univ. (Germany). Fachbereich 3 - Mathematik) Suris and Technische Univ. Berlin (Germany). Sonderforschungsbereich 288 -Differentialgeometrie und Quantenphysik

Abstract

Discretizations of the Euler top sharing the integrals of motion with the continuous time system are studied. Those of them which are also Poisson with respect to the invariant Poisson bracket of the Euler top are characterized. For all these Poisson discretizations a solution in terms of elliptic functions is found, allowing a direct comparison with the continuous time case. We demonstrate that the Veselov-Moser discretization also belongs to our family, and apply our methods to this particular example. (orig.)Available from TIB Hannover: RR 1596(312) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Topics: 12A - Pure mathematics, DYNAMICAL SYSTEMS, INTEGRABLE DISCRETIZATIONS, EULER TOP, VESELOV-MOSER SYSTEM, POISSON STRUCTURE, LAX REPRESENTATION, CONTINUOUS TIME SYSTEM
Year: 1998
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Provided by: OpenGrey Repository
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