论文标题
经典的多院汉密尔顿系统，可及性和Haantjes几何形状
Classical Multiseparable Hamiltonian Systems, Superintegrability and Haantjes Geometry
论文作者
论文摘要
我们表明，可以在（$ω，\ mathscr {h} $）结构的背景下制定经典哈密顿系统的理论。它们是具有兼容的Haantjes代数$ \ Mathscr {H} $的符号歧管，即（1,1）的代数（1,1） - 带有消失的Haantjes Torsion的代数。将由与可分离系统相关的Haantjes代数构建的一种特殊类别的坐标，称为Darboux-Haantjes坐标。这些坐标使相应的汉密尔顿 - 雅各比方程的变量的添加性分离。 我们将证明，多层系统将与分隔坐标系一样多$ω\ Mathscr {H} $结构。特别是，我们将表明，一大批可培训的可促进系统，包括Smorodinsky-Winternitz系统和一些具有三个自由度的物理相关系统，具有多个Haantjes结构。
We show that the theory of classical Hamiltonian systems admitting separating variables can be formulated in the context of ($ω, \mathscr{H}$) structures. They are symplectic manifolds endowed with a compatible Haantjes algebra $\mathscr{H}$, namely an algebra of (1,1)-tensor fields with vanishing Haantjes torsion. A special class of coordinates, called Darboux-Haantjes coordinates, will be constructed from the Haantjes algebras associated with a separable system. These coordinates enable the additive separation of variables of the corresponding Hamilton-Jacobi equation. We shall prove that a multiseparable system admits as many $ω\mathscr{H}$ structures as separation coordinate systems. In particular, we will show that a large class of multiseparable, superintegrable systems, including the Smorodinsky-Winternitz systems and some physically relevant systems with three degrees of freedom, possesses multiple Haantjes structures.
