We prove differentiability of certain linear combinations of the Lyapunov spectra of a flow on a principal bundle of a semi-simple Lie group. The specific linear combinations that yield differentiability are determined by the finest Morse decomposition on the flag bundles. Differentiability is taken with respect to a differentiable structure on the gauge group, which is a Banach-Lie group.

中文翻译：

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李雅普诺夫指数的可微性

我们证明了半简单Lie群的主束上流的Lyapunov谱的某些线性组合的可微性。产生微分性的特定线性组合由标志束上最精细的摩尔斯分解确定。关于量规组（即Banach-Lie组）上的可微结构，采取了可微性。