The linear request problem

Benoît Kloeckner (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

This article propose an alternative approach to a problem introduced by Galatolo and Pollicott, consisting in perturbing a dynamical system in order for its absolutely continuous invariant measure ("acim" , assumed to exist) to change in a prescribed way. Instead of using transfer operators, we rely on the continuity equation to produce a perturbation of the system which is an infinitesimal conjugacy. This allows us to work in any dimension and dispense from any dynamical hypothesis. In particular, we don't need to assume the dynamical system is hyperbolic; but if it is, we obtain our acim-prescribed perturbations within this class.

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

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

Benoît Kloeckner. The linear request problem. 2016. ⟨hal-01327440v1⟩