We describe an atlas adapted to the Toda flow on the manifold of full flags of any non-compact real semisimple Lie algebra and on its Hessenberg-type submanifolds. We show that in the local coordinates of the atlas the Toda flow becomes linear. The local coordinates are also used to show that the Toda flow on the manifold of full flags is Morse–Smale, which generalizes the result for traceless matrices in [27] to arbitrary non-compact real semisimple Lie algebras. As a byproduct we describe new features of classical constructions in matrix theory.

中文翻译：

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适应户田流的地图集

我们描述了一个适用于任何非紧实半单李代数的满旗流形及其 Hessenberg 型子流形上的 Toda 流的图集。我们表明，在地图集的局部坐标中，Toda 流变为线性。局部坐标也用于表明满旗流形上的 Toda 流是 Morse-Smale，这将 [27] 中的无迹矩阵的结果推广到任意非紧实半单李代数。作为副产品，我们描述了矩阵理论中经典结构的新特征。