Related papers: Length functions on currents and applications to d…

We study partially hyperbolic diffeomorphisms satisfying a trapping property which makes them look as if they were Anosov at large scale. We show that, as expected, they share several properties with Anosov diffeomorphisms. We construct an…

We know from previous work with Italiano and Migliorini that there exists some hyperbolic 5-manifold that fibers over the circle. Here we build one example where the monodromy is a "pseudo-Anosov homeomorphism" of the 4-dimensional fiber,…

Let $M$ be a closed 3-manifold which admits an Anosov flow. In this paper we develop a technique for constructing partially hyperbolic representatives in many mapping classes of $M$. We apply this technique both in the setting of geodesic…

We extend results of parametric geometry of numbers to a general diagonal flow on the space of lattices. Moreover, we compute the Hausdorff dimension of the set of trajectories with every given behavior, with respect to a nonstandard metric…

We first prove rigidity results for pseudo-Anosov flows in prototypes of toroidal 3-manifolds: we show that a pseudo-Anosov flow in a Seifert fibered manifold is up to finite covers topologically equivalent to a geodesic flow and we show…

We construct a H\"older continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1 passing through the origin. We say that a function with…

We study functions which are the pointwise limit of a sequence of holomorphic functions. In one complex variable this is a classical topic, though we offer some new points of view and new results. Some novel results for solutions of…

For every positive, continuous and homogeneous function $f$ on the space of currents on a compact surface $\overline{\Sigma}$, and for every compactly supported filling current $\alpha$, we compute as $L \to \infty$, the number of mapping…

In this paper, we study ergodic optimization of continuous functions for flows by concentrating on the entropy spectrum of their maximizing measures. Precisely, over a wide family of flows with non-uniformly hyperbolic structure, we obtain…

This master thesis looks at the gradient flow of the length functional on embedded loops. The space of embedded loops is endowed with a scale structure so that the length functional becomes scale smooth. For certain underlying manifolds,…

The purpose of this paper is to give a short microlocal proof of the meromorphic continuation of the Ruelle zeta function for C^\infty Anosov flows. More general results have been recently proved by Giulietti-Liverani-Pollicott…

We discuss some properties of the distance functions on Riemannian manifolds and we relate their behavior to the geometry of the manifolds. This leads to alternative proofs of some "classical" theorems connecting curvature and topology.

In [Grenier-Nguyen], we introduced so called {\em generators} functions to precisely follow the regularity of analytic solutions of Navier Stokes equations. In this short note, we give a presentation of these generator functions and use…

We introduce topological definitions of expansivity, shadowing, and chain recurrence for homeomorphisms. They generalize the usual definitions for metric spaces. We prove various theorems about topologically Anosov homeomorphisms (maps that…

We present a construction of sequences of closed hyperbolic surfaces that have long systoles which form pants decompositions of these surfaces. The length of the systoles of these surfaces grows logarithmically as a function of their genus.

Some features of extended loops are considered. In particular, the behaviour under diffeomorphism transformations of the wavefunctions with support on the extended loop space are studied. The basis of a method to obtain analytical…

Understanding the nanoscale effects controlling the dynamics of a contact line -- defined as the line formed at the junction of two fluid phases and a solid -- has been a longstanding problem in fluid mechanics pushing experimental and…

In this short note, we prove that all geodesically convex functions defined on a Riemannian manifold are continuous in the interior of their domain. This is a folklore result, but to the best of our knowledge, there is only one available…

We study counting limit laws that compare length functions on infinite graphs. We then apply these results to flat surfaces to obtain a statistical comparison between the geometric length and the number of singularities visited by geodesic…

We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.