The linear request problem

Benoît Kloeckner (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We propose a simple approach to a problem introduced by Galatolo and Pollicott, consisting in perturbing a dynamical system in order for its absolutely continuous invariant measure to change in a prescribed way. Instead of using transfer operators, we observe that restricting to an infinitesimal conjugacy already yields a solution. This allows us to work in any dimension and dispense from any dynamical hypothesis. In particular, we don’t need to assume hyperbolicity to obtain a solution, although expansion moreover ensures the existence of an infinite-dimensional space of solutions.

Mots clés: linear response; invariant measure; continuity equation; conjugacy

Domaines: Systèmes dynamiques [math.DS]; Géométrie différentielle [math.DG]

Benoît Kloeckner. The linear request problem. Proceedings of the American Mathematical Society, 2018, 146 (7), pp.2953-2962. ⟨10.1090/proc/14026⟩. ⟨hal-01327440v2⟩