论文标题
$ω$ -HAMILTONIAN矢量字段的正常形式与对称性
Normal forms of $ω$-Hamiltonian vector fields with symmetries
论文作者
论文摘要
在本文中，我们提出了代数工具，以通过考虑矢量场的对称性和逆转对称性，以在谎言组的半透明动作下获得$ω$ -HAMILTONIAN矢量场的正常形式。该过程产生的正常形式保留了哈密顿条件和原始矢量场的对称性类型。我们的技术将哈密顿载体场的正常形式的经典方法与群体的不变理论结合在一起。
In this paper, we present algebraic tools to obtain normal forms of $ω$-Hamiltonian vector fields under a semisymplectic action of a Lie group, by taking into account the symmetries and reversing symmetries of the vector field. The normal forms resulting from the process preserve the Hamiltonian condition and the types of symmetries of the original vector field. Our techniques combine the classical method of normal forms of Hamiltonian vector fields with the invariant theory of groups.
