Hamiltonian systems on almost cosymplectic manifolds

Abstract

We determine the Hamiltonian vector field on an odd dimensional manifold endowed with almost cosymplectic structure. This is a generalization of the corresponding Hamiltonian vector field on manifolds with almost transitive contact structures, which extends the contact Hamiltonian systems. Applications are presented to the equations of motion on a particular five-dimensional manifold, the extended Siegel-Jacobi upper-half plane ${\tilde{\mathcal{X}}}_1^J$. The ${\tilde{\mathcal{X}}}_1^J$ manifold is endowed with a generalized transitive almost cosymplectic structure, an almost cosymplectic structure, more general than transitive almost contact structure and cosymplectic structure.The equations of motion on ${\tilde{\mathcal{X}}}_1^J$ extend the Riccati equations of motion on the four-dimensional Siegel-Jacobi manifold ${\mathcal{X}}_1^J$ attached to a linear Hamiltonian in the generators of the real Jacobi group $G_1^J(\mathbb{R})$.

27 pages, Latex, amsart, AMS fonts, the appendix is systematized, one more reference is added, some typos are corrected

References in corpus (8)

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• The Real Jacobi Group Revisited
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