We show that the theory of classical Hamiltonian systems admitting separating variables can be formulated in the context of ($\omega ,\mathcal{H}$) structures. They are symplectic manifolds endowed with a compatible Haantjes algebra $\mathcal{H}$, 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 $\omega \mathcal{H}$ 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.

我们表明，允许分离变量的经典哈密顿系统的理论可以在（$\omega ,\mathcal{H}$) 结构。它们是具有相容 Haantjes 代数的辛流形$\mathcal{H}$，即具有消失的 Haantjes 扭转的 (1,1) 张量场的代数。一类特殊的坐标，称为 Darboux-Haantjes 坐标，将由与可分离系统相关的 Haantjes 代数构造。这些坐标使相应的 Hamilton-Jacobi 方程的变量能够相加分离。

我们将证明一个多可分系统允许尽可能多的 $\omega \mathcal{H}$结构作为分离坐标系。特别是，我们将证明一大类多重可分、超可积系统，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。