Amir Algom

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20162024

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math.DS2024

On the dimension of orthogonal projections of self-similar measures

Amir Algom, Pablo Shmerkin

Let $ν$ be a self similar measure on $R^{d}$ , $d \geq 2$ , and let $π$ be an orthogonal projection onto a $k$ -dimensional subspace. We formulate a criterion on the action of t…

math.DS2024

Van der Corput and metric theorems for geometric progressions for self-similar measures

Amir Algom, Yuanyang Chang, Meng Wu +1

We prove a van der Corput lemma for non-atomic self-similar measures $μ$ . As an application, we show that the correlations of all finite orders of $(x^{n} mod 1)_{n \geq 1}$ conver…

math.DS2023

Large slices through self affine carpets

Amir Algom, Meng Wu

Let $F \subseteq [0, 1]^{2}$ be a Bedford-McMullen carpet defined by exponents $m > n$ , that projects to $[0, 1]$ on the $y$ -axis. We show that under mild conditions on $F$ , there are man…

math.DS2016

Affine embeddings of Cantor sets on the line

Amir Algom

Let $s \in (0, 1)$ , and let $F \subset R$ be a self similar set such that $0 < dim_{H} F \leq s$ . We prove that there exists $δ = δ (s) > 0$ such that if $F$ admits an affine em…