Action-Angle variables on Dirac manifolds

Details Action-Angle variables on Dirac manifolds Action-Angle variables on Dirac manifolds

2012-04-17

arxiv.org/abs/1204.3865v1

Mathematics

Symplectic Geometry

22 pages

Scientific paper

The main purpose of this paper is to show the existence of action-angle variables for integrable Hamiltonian systems on Dirac manifolds under some natural regularity and compactness conditions, using the torus action approach. We show that the Liouville torus actions of general integrable dynamical systems have the structure-preserving property with respect to any underlying geometric structure of the system, and deduce the existence of action-angle variables from this property. We also discover co-affine structures on manifolds as a by-product of our study of action-angle variables. 22 pages.

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