8 citations · 16 across the 8 of their papers we have counts for
14 papers
Higher genus Cherry flows and full families of GIETs
Luca Marchese, Liviana Palmisano
Cherry flows are classical examples of flows on the two-dimensional torus exhibiting non-trivial recurrent dynamics. For every genus we construct a p…
On the measure of products from the middle-third Cantor set
Luca Marchese
We prove upper and lower bounds for the Lebesgue measure of the set of products with and in the middle-third Cantor set. Our method is inspired by Athreya, Reznick and…
A genus 4 origami with minimal hitting time and an intersection property
Luca Marchese
In a minimal flow, the hitting time is the exponent of the power law, as r goes to zero, for the time needed by orbits to become r-dense. We show that on the so-called Ornithorynqu…
On good approximations and Bowen-Series expansion
Luca Marchese
We consider the continued fraction expansion of real numbers under the action of a non-uniform lattice in PSL(2,R) and prove metric relations between the convergents and a natural…
Transfer operators and dimension of bad sets for non-uniform Fuchsian lattices
Luca Marchese
The set of real numbers which are badly approximable by rationals admits an exhaustion by sets Bad(), whose dimension converges to 1 as goes to zero. D. Hensley computed the…
Persistent Hall rays for Lagrange spectra at cusps of Riemann surfaces
Mauro Artigiani, Luca Marchese, Corinna Ulcigrai
We study Lagrange spectra at cusps of finite area Riemann surfaces. These spectra are penetration spectra that describe the asymptotic depths of penetration of geodesics in the cus…
Full families of generalized interval exchange transformations
Luca Marchese, Liviana Palmisano
We consider generalized interval exchange transformations, or briefly GIETs, that is bijections of the interval which are piecewise increasing homeomorphisms with finite branches.…
Long Hitting time for translation flows and L-shaped billiards
Dong Han Kim, Luca Marchese, Stefano Marmi
We consider the flow in direction on a translation surface and we study the asymptotic behavior for of the time needed by orbits to hit the -neighborhood of a presc…
The Lagrange spectrum of some square-tiled surfaces
Pascal Hubert, Samuel Lelièvre, Luca Marchese +1
Lagrange spectra have been defined for closed submanifolds of the moduli space of translation surfaces which are invariant under the action of SL(2,R). We consider the closed orbit…
Diophantine approximations for translation surfaces and planar resonant sets
Luca Marchese, Rodrigo Treviño, Steffen Weil
We consider Teichmüller geodesics in strata of translation surfaces. We prove lower and upper bounds for the Hausdorff dimension of the set of parameters generating a geodesic boun…
The Lagrange spectrum of a Veech surface has a Hall ray
Mauro Artigiani, Luca Marchese, Corinna Ulcigrai
We study Lagrange spectra of Veech translation surfaces, which are a generalization of the classical Lagrange spectrum. We show that any such Lagrange spectrum contains a Hall ray.…
Lagrange Spectra in Teichmüller Dynamics via renormalization
Pascal Hubert, Luca Marchese, Corinna Ulcigrai
We introduce Lagrange Spectra of closed-invariant loci for the action of SL(2,R) on the moduli space of translation surfaces, generalizing the classical Lagrange Spectrum, and we a…
Khinchin type condition for translation surfaces and asymptotic laws for the Teichmuller flow
Luca Marchese
We study a diophantine property for translation surfaces, defined in term of saddle connections and inspired by the classical theorem of Khinchin. We prove that the same dichotomy…
Khinchin theorem for interval exchange transformations
Luca Marchese
We define a diophantine condition for interval exchange transformations (i.e.t.s). When the number of intervals is two, that is for rotations on the circle, our condition coincides…