53 citations · 235 across the 32 of their papers we have counts for
12 papers · 1 filter
A new orbit closure in genus 8?
Delecroix Vincent, Rüth Julian
We provide numerical evidence that the orbit closure of the unfolding of the -triangle is a previously unknown 4-dimensional variety.
Diagonal flow detects topology of strata
Mark Bell, Vincent Delecroix, Vaibhav Gadre +2
We study the interplay between the diagonal flow on, and the topology of, a stratum component of a space of rooted quadratic differentials. We prove that the flow group -- the subg…
Coding Teichmüller flow using veering triangulations
Mark Bell, Vincent Delecroix, Vaibhav Gadre +2
We develop the theory of veering triangulations on oriented surfaces adapted to moduli spaces of half-translation surfaces. We use veering triangulations to give a coding of the Te…
Approximation of the Lagrange and Markov spectra
Vincent Delecroix, Carlos Matheus, Carlos Gustavo Moreira
The (classical) Lagrange spectrum is a closed subset of the positive real numbers defined in terms of diophantine approximation. Its structure is quite involved. This article descr…
From a Packing Problem to Quantitative Recurrence in and the Lagrange Spectrum of Interval Exchanges
Michael Boshernitzan, Vincent Delecroix
This article provides optimal constants for two quantitative recurrence problems. First of all for recurrence of maps of the interval [0,1] that preserve the Lebesgue measure and o…
Some monoids of Pisot matrices
Artur Avila, Vincent Delecroix
We show that several monoids of non-negative integer matrices enjoy a Pisot property: each matrix in that monoid has only one eigenvalue with absolute value larger than one. These…
Cries and whispers in wind-tree forests
Vincent Delecroix, Anton Zorich
We study billiard in the plane endowed with symmetric $\mathbb{Z}^2$-periodic obstacles of a right-angled polygonal shape. One of our main interests is the dependence of the diff…
Diagonal changes for surfaces in hyperelliptic components
Vincent Delecroix, Corinna Ulcigrai
We describe geometric algorithms that generalize the classical continued fraction algorithm for the torus to all translation surfaces in hyperelliptic components of translation sur…
Beyond substitutive dynamical systems: S-adic expansions
Valérie Berthé, Vincent Delecroix
An S-adic expansion of an infinite word is a way of writing it as the limit of an infinite product of substitutions (i.e., morphisms of a free monoid). Such a description is relate…
Weak mixing directions in non-arithmetic Veech surfaces
Artur Avila, Vincent Delecroix
We show that the billiard in a regular polygon is weak mixing in almost every invariant surface, except in the trivial cases which give rise to lattices in the plane (triangle, squ…
Divergent directions in some periodic wind-tree models
Vincent Delecroix
The periodic wind-tree model is a family T(a,b) of billiards in the plane in which identical rectangular scatterers of size axb are disposed at each integer point. It was proven by…
Diffusion for the periodic wind-tree model
Vincent Delecroix, Pascal Hubert, Samuel Lelièvre
The periodic wind-tree model is an infinite billiard in the plane with identical rectangular scatterers disposed at each integer point. We prove that independently of the size of t…