We study the cohomological equation associated to linear cocycles on semi simple Lie groups $\mathcal G$ over hyperbolic dynamics. We give sufficient conditions for the solution of the cohomological equation of fiber-bunched cocycles to be unique and for the Hölder conjugacy class of the cocycle to coincide with $C^\nu(M,\mathcal G)$. In particular, we prove that there exists an open and dense subset of the set $C_b^\nu(M,\mathcal G)$ of fiber-bunched cocycles with trivial centralizer. As a consequence we deduce that the solutions of the {cohomological} equation of fiber-bunched cocycles form a finite abelian subgroup of $C_b^\nu(M,\mathcal G)$ for an open and dense subset of fiber-bunched cocycles in $C_b^\nu(M,\mathcal G)$. Some results on the centralizer of skew-products are also given.

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关于半简单李群上纤维束缚的同轮摩托车的同调类

我们研究了双曲动力学上半简单李群$ \数学G $上与线性循环相关的同调方程。我们给出了充分的条件，以使纤维束缚的三轮车的同调方程的解唯一，并且使该三轮车的Hölder共轭类与$ C ^ \ nu（M，\ mathcal G）$一致。尤其是，我们证明存在带有琐碎扶正器的纤维束缚的联合循环$ C_b ^ \ nu（M，\ mathcal G）$集的一个开放且密集的子集。结果，我们推导了纤维束缚的cocycles的{cohomological}方程的解形成了一个有限的阿贝尔亚群，其中C是一个密集的子集，其中C = b ^ \ nu（M，\ mathcal G）$。 $ C_b ^ \ nu（M，\ mathcal G）$。还给出了偏积的扶正器的一些结果。