3 papers
math.DS2022
Pairs of saddle connections of typical flat surfaces on fixed affine orbifolds
Etienne Bonnafoux
We prove that the asymptotic number of pairs of saddle connections with length smaller than with bounded virtual area is quadratic for almost every translation surface with res…
math.DS2022
Arithmeticity of the Kontsevich--Zorich monodromies of certain families of square-tiled surfaces
Etienne Bonnafoux, Manuel Kany, Pascal Kattler +5
The variations of Hodge structures of weight one associated to square-tiled surfaces naturally generate interesting subgroups of integral symplectic matrices called Kontsevich--Zor…
math.DS2022
Upper bound on the rate of mixing for the Earthquake flow on moduli spaces
Etienne Bonnafoux
We prove that the earthquake flow is at most polynomially mixing with a degree bounded by a constant depending only on the topology of the surface. In particular it is not exponent…