ABSTRACT:

Abstract: We are concerned with the question of the differentiability of the SRB measure mu_t associated to a path of discrete-time dynamics f_t. With Daniel Smania we discovered in 2007 that differentiability at 0 holds if and only if the path is tangent to the topological class at 0, in the piecewise expanding setting. When differentiability holds, we can write a formula for the derivative (the linear response formula). After recalling this result, we shall present our new results on Colle-Eckmann maps.