Goldman parametrizes the $\operatorname{PSL}_3(\mathbb{R})$-Hitchin component of a closed oriented hyperbolic surface of genus $g$ by $16g - 16$ parameters. Among them, $10g - 10$ coordinates are canonical. We prove that the $\operatorname{PSL}_3(\mathbb{R})$-Hitchin component equipped with the Atiyah–Bott–Goldman symplectic form admits a global Darboux coordinate system such that the half of its coordinates are canonical Goldman coordinates. To this end, we show a version of the action-angle principle and the Zocca-type decomposition formula for the symplectic form of H. Kim and Guruprasad–Huebschmann–Jeffrey-Weinstein given to symplectic leaves of the Hitchin component.

中文翻译：

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$ \ operatorname {PSL} _3（\ mathbb {R}）$-Hitchin分量上的辛坐标

高盛用$ 16g-16 $参数对$ g $属的闭合定向双曲曲面的$ \ operatorname {PSL} _3（\ mathbb {R}）$-Hitchin分量进行参数化。其中，$ 10g-10 $坐标是标准的。我们证明，配备Atiyah-Bott-Goldman辛格式的$ \ operatorname {PSL} _3（\ mathbb {R}）$-Hitchin分量承认一个全局Darboux坐标系，因此其一半坐标是规范的Goldman坐标。为此，我们为希钦成分的辛叶展示了H. Kim和Guruprasad–Huebschmann–Jeffrey-Weinstein辛形式的辛格形式的作用角原理和Zocca型分解公式。