A Class of Integrable Geodesic Flows on the Symplectic Group
نویسندگان
چکیده
In this paper we show that the left-invariant geodesic flow on the symplectic group with metric given by the Frobenius norm is an integrable system that is not contained in the Mishchenko-Fomenko class. We show that this system may be expressed as a flow on symmetric matrices and that the system is biHamiltonian. Research partially supported by the NSF. Research partially supported by the California Institute of Technology and NSF. Research partially supported by the Swiss NSF.
منابع مشابه
A Class of Integrable Geodesic Flows on the Symplectic Group and the Symmetric Matrices
This paper shows that the left-invariant geodesic flow on the symplectic group relative to the Frobenius metric is an integrable system that is not contained in the Mishchenko-Fomenko class of rigid body metrics. This system may be expressed as a flow on symmetric matrices and is bi-Hamiltonian. This analysis is extended to cover flows on symmetric matrices when an isomorphism Research partiall...
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