Alexandro Luna

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math.DS2026

On Sums of "Small" Cantor Sets

Anton Gorodetski, Alexandro Luna, William Wood

We provide several results showing that sums of ``small'' Cantor sets can turn into an interval or a finite union of intervals. Specifically, we show that 1) There exists a Cantor…

math.DS2022

Thomae's function and the space of ergodic measures

Anton Gorodetski, Alexandro Luna

We study the space of ergodic measures of the map $f : T^{2} \to T^{2}, f (x, y) = (x, x + y) (mod 1),$ and show that its structure is similar to the graph of T…