8 papers
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…
Generic dynamical properties of connections on vector bundles
Mihajlo Cekić, Thibault Lefeuvre
Given a smooth Hermitian vector bundle over a closed Riemannian manifold , we study generic properties of unitary connections on the vec…
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…
Classical and microlocal analysis of the X-ray transform on Anosov manifolds
Sébastien Gouëzel, Thibault Lefeuvre
We complete the microlocal study of the geodesic X-ray transform on Riemannian manifolds with Anosov geodesic flow initiated by Guillarmou and pursued by Guillarmou and the second…
On the s-injectivity of the X-ray transform on manifolds with hyperbolic trapped set
Thibault Lefeuvre
For smooth compact connected manifolds with strictly convex boundary, no conjugate points and a hyperbolic trapped set, we prove an equivalence principle concerning the injectivity…
The marked length spectrum of Anosov manifolds
Colin Guillarmou, Thibault Lefeuvre
In all dimensions, we prove that the marked length spectrum of a Riemannian manifold with Anosov geodesic flow and non-positive curvature locally determines the metric in t…