We introduce a new strategy to prove simplicity of the spectrum of Lyapunov exponents that can be applied to a wide class of Markovian multidimensional continued fraction algorithms. As an application we use it for Selmer algorithm in dimension 2 and for the Triangle sequence algorithm and show that these algorithms are not optimal.

中文翻译：

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某些多维连续分数算法的光谱简单性

我们引入了一种新的策略来证明Lyapunov指数谱的简单性，可以将其应用于广泛的Markovian多维连续分数算法。作为应用程序，我们将其用于2维的Selmer算法和Triangle序列算法，并证明这些算法不是最佳算法。