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Graph theory and a special class of symplectic transformations: The generalized Jacobi variables (1991)

Lim, Chjan C.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 32 (1991), S. 1-7

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: The well-known Jacobi variables in celestial mechanics are generalized to other Hamiltonian systems which include vortex dynamics. A combinatorial algorithm for constructing the generalized Jacobi variables is given; for any binary tree T(N) with N leave, there is a 2N×2N real symplectic matrix MT (T(N),Γ) which completely defines a linear canonical transformation to these relative variables. This algorithm yields a direct proof of the symplectic property for all the generalized Jacobi variables. An application to vortex dynamics is outlined here.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.529119

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