Abstract: In this talk, we shall discuss the following two problems: (1) the response formulae of any order for the absolutely continuous invariant probabilities (ACIP’s) for smooth expanding endomorphisms, with applications to its inverse problem - the request problem, i.e. the search of perturbations for prescribed variations of ACIP densities; (2) the explicit formula of linear response for equilibrium measures of piecewise expanding unimodal maps. The basic tool is the differentiability of thermodynamic quantities related to the transfer operators.
