32 citations · 62 across the 20 of their papers we have counts for
20 papers
Chaoticity of generic analytic convex billiards
Inmaculada Baldomá, Anna Florio, Martin Leguil +1
We show that a generic analytic strongly convex billiard is "maximally chaotic" in the sense that, for every rational number , all intersecti…
Extremal distributions of partially hyperbolic systems: the Lipschitz threshold
Martin Leguil, Disheng Xu, Jiesong Zhang
We prove a sharp phase transition in the regularity of the extremal distribution for volume-preserving partially hyperbolic diffeomorphisms on closed $3…
Deformation and perturbative rigidity near de la Llave examples
Andrey Gogolev, Martin Leguil
De la Llave's examples are Anosov diffeomorphisms on the four-torus with constant Lyapunov spectrum, yet they are not -conjugate to the linear model or to eac…
On the rigidity of the stable norm and Mather's β-function for geodesic flows
Anna Florio, Martin Leguil, Alfonso Sorrentino
We investigate rigidity phenomena associated to the stable norm and Mather's -function for Riemannian geodesic flows on closed manifolds. Given two metrics and , we c…
Smooth rigidity for 3-dimensional dissipative Anosov flows
Andrey Gogolev, Martin Leguil, Federico Rodriguez Hertz
We consider two transitive -dimensional Anosov flows which do not preserve volume and which are continuously conjugate to each other. Then, disregarding certain exceptional case…
A CAT(0)-approach to the marked length spectral rigidity of Sinai billiards
Douglas Finamore, Martin Leguil
We study the spectral rigidity problem for Sinai billiards with finite horizon, specifically asking whether the geometry of the billiard table can be recovered from the lengths of…
Birkhoff attractors of dissipative billiards
Olga Bernardi, Anna Florio, Martin Leguil
We study the dynamics of dissipative billiard maps within planar convex domains. Such maps have a global attractor. We are interested in the topological and dynamical complexity of…
Rigidity of -Gibbs measures near conservative Anosov diffeomorphisms on
Sébastien Alvarez, Martin Leguil, Davi Obata +1
We show that within a -neighbourhood of the set of volume preserving Anosov diffeomorphisms on the three-torus which are strongly partially hyperb…
Accessibility for dynamically coherent partially hyperbolic diffeomorphisms with 2D center
Martin Leguil, Luis Pedro Piñeyrúa
We show that for any integer , stable accessibility is -dense among partially hyperbolic diffeomorphisms with two-dimensional center that satisfy some strong bunchin…
Smooth conjugacy classes of 3D Axiom A flows
Anna Florio, Martin Leguil
We show a rigidity result for 3-dimensional contact Axiom A flows: given two 3D contact Axiom A flows whose restrictions to basic sets a…
Invariant graphs and spectral type of Schrödinger operators
Artur Avila, Konstantin Khanin, Martin Leguil
In this paper we study spectral properties of Schrödinger operators with quasi-periodic potentials related to quasi-periodic action minimizing trajectories for analytic twist maps.…
Entropy rigidity for 3D conservative Anosov flows and dispersing billiards
Jacopo De Simoi, Martin Leguil, Kurt Vinhage +1
Given an integer , and a Anosov flow on some compact connected -manifold preserving a smooth volume, we show that the measure of maximal entropy (MME) is the…
Marked Length Spectral determination of analytic chaotic billiards with axial symmetries
Jacopo De Simoi, Vadim Kaloshin, Martin Leguil
We consider billiards obtained by removing from the plane finitely many strictly convex analytic obstacles satisfying the non-eclipse condition. The restriction of the dynamics to…
On the centralizer of vector fields: criteria of triviality and genericity results
Martin Leguil, Davi Obata, Bruno Santiago
In this paper, we investigate the question of whether a typical vector field on a compact connected Riemannian manifold has a `small' centralizer. In the case, we give…
Marked Length Spectrum, homoclinic orbits and the geometry of open dispersing billiards
Péter Bálint, Jacopo De Simoi, Vadim Kaloshin +1
We consider billiards obtained by removing three strictly convex obstacles satisfying the non-eclipse condition on the plane. The restriction of the dynamics to the set of non-esca…
Asymptotics of spectral gaps of quasi-periodic Schrödinger operators
Martin Leguil, Jiangong You, Zhiyan Zhao +1
For non-critical almost Mathieu operators with Diophantine frequency, we establish exponential asymptotics on the size of spectral gaps, and show that the spectrum is homogeneous.…
Exponential decay of the size of spectral gaps for quasiperiodic Schrödinger operators
Martin Leguil
In the following we are interested in the spectral gaps of discrete quasiperiodic Schrödinger operators when the frequency is Diophantine, the potential is analytic, and in the sub…
Dynamics of a family of polynomial automorphisms of , a phase transition
Julie Déserti, Martin Leguil
The polynomial automorphisms of the affine plane have been studied a lot: if is such an automorphism, then either preserves a rational fibration, has an uncountable central…
Weak mixing properties of interval exchange transformations and translation flows
Artur Avila, Martin Leguil
Let . In this paper we show that for an irreducible permutation which is not a rotation, the set of such that the interval exchange transforma…
prevalence of stable ergodicity for a class of partially hyperbolic systems
Martin Leguil, Zhiyuan Zhang
We prove that for , for any dynamically coherent, center bunched and strongly pinched volume preserving partially hyperbolic diffeo…