论文标题
在几乎偶然歧管上的哈密顿系统
Hamiltonian systems on almost cosymplectic manifolds
论文作者
论文摘要
我们在具有几乎固定结构的奇数歧管上确定了哈密顿矢量场。这是对相应的汉密尔顿载体场的概括，并具有几乎传递的接触结构，从而扩展了接触式汉密尔顿系统。将应用程序显示在特定五维流形的运动方程式，即扩展的Siegel-Jacobi上半平面$ \ tilde {\ Mathcal {X}}}^J_1 $。 $ \ tilde {\ Mathcal {x}}^J_1 $歧管具有通用的传递几乎几乎固定的结构，几乎是固定的结构，比传递几乎几乎几乎是接触结构和偶像结构更通用。在真实的jacobi组$ g^j_1（\ mathbb {r}）$的生成器中，将四维siegel-jacobi歧管$ \ mathcal {x}^j_1 $连接到线性汉密尔顿。
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 $\tilde{\mathcal{X}}^J_1$. The $\tilde{\mathcal{X}}^J_1$ 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 $\tilde{\mathcal{X}}^J_1$ extend the Riccati equations of motion on the four-dimensional Siegel-Jacobi manifold $\mathcal{X}^J_1$ attached to a linear Hamiltonian in the generators of the real Jacobi group $G^J_1(\mathbb{R})$.
