Revista de la
Unión Matemática Argentina
Perturbation of Ruelle resonances and Faure–Sjöstrand anisotropic space
Yannick Guedes Bonthonneau
Volume 61, no. 1 (2020), pp. 63–72

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Given an Anosov vector field $X_0$, all sufficiently close vector fields are also of Anosov type. In this note, we check that the anisotropic spaces described by Faure and Sjöstrand and by Dyatlov and Zworski can be chosen adapted to any smooth vector field sufficiently close to $X_0$ in $C^1$ norm.