R\'eponse lin\'eaire et points p\'eriodiques : cas analytique

We explain some points of the demonstration by Pollicott and Vytnova of a formula for linear response in terms of periodic points in the case of analytic expanding maps of the circle or Anosov diffeomorphisms of the torus. The main tool is the dynamical determinant which may be written as the Fredholm determinant of a transfer operator (or a quotient of Fredholm determinants of transfer operators).