Flow-independent Anisotropic space, and perturbation of resonances

Yannick Guedes Bonthonneau

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arXiv · 1806.08125

Flow-independent Anisotropic space, and perturbation of resonances

Yannick Guedes Bonthonneau

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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-Sj\"ostrand" 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.

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Yannick Guedes Bonthonneau. 2018-06-21. Flow-independent Anisotropic space, and perturbation of resonances. https://arxiv.org/abs/1806.08125

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