Flow-independent Anisotropic space, and perturbation of resonances

Abstract

Given an Anosov vector field $X_0$, all sufficiently close vector fields also are of Anosov type. In this note, we check that one can choose the so-called "Faure-Sjöstrand" anistropic spaces to be adapted to any smooth vector field sufficiently close to $X_0$ in $C^1$ norm. It follows that finite families of resonances depend smoothly on the vector field with the usual caveats. In this second version, more details are given on the perturbation of spectral projectors.

10 pages