8 citations · 45 across the 21 of their papers we have counts for
26 papers
The Yang-Mills measure on surfaces via Morse theory
Reda Chhaibi, Nguyen Viet Dang, Yannick Guedes Bonthonneau +2
We introduce a Morse theoretical approach to the construction of the Yang--Mills measure on the space of connections of a compact Riemannian surface. This provides a direct continu…
The spectrum of Anosov representations
Yannick Guedes Bonthonneau, Thibault Lefeuvre, Tobias Weich
Given a -Anosov representation into a noncompact semisimple real algebraic group , where is a parabolic subgroup, we construct a natural resonance spectrum for the cl…
Poincar{é} series for analytic convex bodies
Nguyen Viet Dang, Yannick Guedes Bonthonneau, Matthieu Léautaud +1
We study Poincar{é} series associated to strictly convex bodies in the Euclidean space. These series are Laplace transforms of the distribution of lengths (measured with the Finsle…
Tunneling between magnetic wells in two dimensions
Søren Fournais, Yannick Guedes Bonthonneau, Léo Morin +1
The two-dimensional magnetic Laplacian is considered. We calculate the leading term of the splitting between the first two eigenvalues of the operator in the semiclassical limit un…
Bunching for relatively pinched metrics
Yannick Guedes Bonthonneau
We consider compact Riemannian manifolds whose curvature tensor is pointwise negatively pinched, and improve on the corresponding unstable bunching estimate from Hasselblatt's 1994…
Microlocal Projectors
Yannick Guedes Bonthonneau
The purpose of this article is to study operators whose kernel share some key features of Bergman kernels from complex analysis, and are approximate projectors. It turns out that t…
Extending a result of Chen, Erchenko and Gogolev
Yannick Guedes Bonthonneau
In a recent paper, Chen, Erchenko and Gogolev have proven that if a Riemannian manifold with boundary has hyperbolic geodesic trapped set, then it can be embedded into a compact ma…
Geodesic Lévy flights and expected stopping time for random searches
Yann Chaubet, Yannick Guedes Bonthonneau, Thibault Lefeuvre +1
We give an analytic description for the infinitesimal generator constructed by Applebaum-Estrade for Lévy flights on a broad class of closed Riemannian manifolds including all nega…
Resolvent of vector fields and Lefschetz numbers
Yann Chaubet, Yannick Guedes Bonthonneau
Dynamical series such as the Ruelle zeta function have become a staple in the study of hyperbolic flows. They are usually analyzed by relating them to the resolvent of the vector f…
Scattering rigidity for analytic metrics
Yannick Guedes Bonthonneau, Colin Guillarmou, Malo Jézéquel
For analytic negatively curved Riemannian manifold with analytic strictly convex boundary, we show that the scattering map for the geodesic flow determines the manifold up to isome…
SRB measures for Anosov actions
Yannick Guedes Bonthonneau, Colin Guillarmou, Tobias Weich
Given a general Anosov action on a closed manifold, we study properties of certain invariant measures that have recently been introduced in \cite{BGHW20} using the t…
Radial source estimates in Hölder-Zygmund spaces for hyperbolic dynamics
Yannick Guedes Bonthonneau, Thibault Lefeuvre
We prove a radial source estimate in Hölder-Zygmund spaces for uniformly hyperbolic dynamics (also known as Anosov flows), in the spirit of Dyatlov-Zworski. The main consequence is…
Magnetic WKB constructions on surfaces
Yannick Guedes Bonthonneau, Tho Nguyen Duc, Nicolas Raymond +1
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 assumpti…
FBI Transform in Gevrey Classes and Anosov Flows
Yannick Guedes Bonthonneau, Malo Jézéquel
An analytic FBI transform is built on compact manifolds without boundary, that satisfies all the expected properties. It enables the study of microlocal analytic and Gevrey regular…
Exponential localization in 2D pure magnetic wells
Yannick Guedes Bonthonneau, Nicolas Raymond, San Vũ Ngoc
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 es…
Local rigidity of manifolds with hyperbolic cusps II. Nonlinear theory
Yannick Guedes Bonthonneau, Thibault Lefeuvre
This article is the second in a series of two whose aim is to extend a recent result of Guillarmou-Lefeuvre [arXiv:1806.04218] on the local rigidity of the marked length spectrum f…
Local rigidity of manifolds with hyperbolic cusps I. Linear theory and microlocal tools
Yannick Guedes Bonthonneau, Thibault Lefeuvre
This paper is the first in a series of two articles whose aim is to extend a recent result of Guillarmou-Lefeuvre on the local rigidity of the marked length spectrum from the case…
Flow-independent Anisotropic space, and perturbation of resonances
Yannick Guedes Bonthonneau
Given an Anosov vector field , all sufficiently close vector fields also are of Anosov type. In this note, we check that one can choose the so-called "Faure-Sjöstrand" anistro…
Ruelle-Pollicott Resonances for Manifolds with Hyperbolic Cusps
Yannick Guedes Bonthonneau, Tobias Weich
We present new methods to construct a Ruelle-Pollicott spectrum for the geodesic flow on manifolds with strictly negative curvature and a finite number of hyperbolic cusps.
WKB constructions in bidimensional magnetic wells
Yannick Bonthonneau, Nicolas Raymond
This article establishes, in an analytic framework and in two dimensions, the first WKB constructions describing the eigenfunctions of the pure magnetic Laplacian with low energy w…
A lower bound for the function on manifolds without conjugate points
Yannick Bonthonneau
In this short note, we prove that the usual function on a Riemannian manifold without conjugate points is uniformly bounded from below. This extends a result of Green in two di…
Quantum Ergodicity for Eisenstein functions
Yannick Bonthonneau, Steve Zelditch
A new proof is given of Quantum Ergodicity for Eisenstein Series for cusped hyperbolic surfaces. This result is also extended to higher dimensional examples, with variable curvatur…
Weyl laws for manifolds with hyperbolic cusps
Yannick Bonthonneau
We give Weyl-type estimates on the natural spectral counting function for manifolds with exact hyperbolic cusps. We treat three different cases: without assumption on the compact p…
Resonance-free regions for negatively curved manifolds with cusps
Yannick Bonthonneau
The Laplace-Beltrami operator on cusp manifolds has continuous spectrum. The resonances are complex numbers that replace the discrete spectrum of the compact case. They are the pol…