arXiv subjects

Yannick Guedes Bonthonneau

Publications and source records attributed to Yannick Guedes Bonthonneau.

21 records · Page 2Linked to original sources

arXiv2020

Magnetic WKB constructions on surfaces

This article is devoted to the description of the eigenvalues and eigenfunctions of the magnetic Laplacian in the semiclassical limit via the complex WKB method. Under the assumption that the magnetic field has a unique and non-degenerate minimum, we construct the local complex WKB approximations for eigenfunctions on a general surface. Furthermore, in the case of the Euclidean plane, with a radially symmetric magnetic field, the eigenfunctions are approximated in an exponentially weighted space.

math.SP↗

arXiv2019

Exponential localization in 2D pure magnetic wells

We establish a magnetic Agmon estimate in the case of a purely magnetic single non-degenerate well, by means of the Fourier-Bros-Iagolnitzer transform and microlocal exponential estimates {à} la Martinez-Sj{ö}strand.

math.AP↗

arXiv2019

Flow-independent Anisotropic space, and perturbation of resonances

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.

math.SP↗