Resumen de On the cohomology class of fiber-bunched cocycles on semi simple Lie groups

Paulo Varandas

• We study the cohomological equation associated to linear cocycles on semi simple Lie groups 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 Cν(M,G). In particular, we prove that there exists an open and dense subset of the set Cνb(M,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 Cνb(M,G) for an open and dense subset of fiber-bunched cocycles in Cνb(M,G). Some results on the centralizer of skew-products are also given.