2 citations · 2 across the 3 of their papers we have counts for
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Mixing of the BCZ Map
Albert Artiles, Andrew Best, Matteo Bordignon
We prove that the Boca--Cobeli--Zaharescu (BCZ) map is strongly mixing with respect to normalized Lebesgue measure on the BCZ triangle.
Moments of the Cross-Sectional Siegel-Veech Transfrom
Albert Artiles
We study the Siegel--Veech transform on the Poincaé section for the horocycle flow consisting of lattice surfaces with a visible horizontal holonomy vector of length at most one. W…
Moments of the Cross-Sectional Siegel-Veech Transform
Albert Artiles
We study the Siegel--Veech transform on the Poincaré section for the horocycle flow consisting of lattice surfaces with a visible horizontal holonomy vector of length at most one.…
The Return Map of the Cross Section of Horizontally Short Lattice Surfaces is Weakly Mixing
Albert Artiles
We prove that the return map of the unstable horocycle flow on the space of horizontally short translation surfaces associated to a lattice surface is weakly mixing. This…
The Minimal Denominator Function and Geometric Generalizations
Albert Artiles
We provide a geometric interpretation for a normalized version of the minimal denominator function, $$q_{\min}(x,δ)=\min\left\{q\in \mathbb{N}: \text{ there exists } p\in\mathbb{Z}…