Abstract
In the class of symplectic matrices, two infinite subsets are generated by binary spanning trees. For given N, the procedure begins with the complete graph, K N to which N-1 virtual vertices are added in well-defined ways. Then spanning binary trees that connect the 2 N-1 vertices are obtained and from these trees, explicit formulae give the symplectic matrices. These matrices define linear canonical transformations for N-body problems in vortex dynamics, plasma physics as well as celestial mechanics.
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