Hamiltonian systems on almost cosymplectic manifolds

DOI10.1016/J.GEOMPHYS.2022.104700arXiv2201.01962MaRDI QIDQ6387618

Stefan Berceanu

Publication date: 6 January 2022

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 $ilde{mathcalX}_1^J$. The $ilde{mathcalX}_1^J$ 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 $ilde{mathcalX}_1^J$ 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 $G_1^J(mathbbR)$.

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Hamilton's equations (70H05) Almost contact and almost symplectic manifolds (53D15) Canonical transformations in symplectic and contact geometry (53D22) Contact systems (37J55) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

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