Michael Hochman

activity

20152025

most citedOn self-similar sets with overlaps and inverse theorems for entropy in

R^{d}

24 citations · 24 across the 6 of their papers we have counts for

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6 papers · 1 filter

math.DS2025

A threshold for Poisson behavior of non-stationary product measures

Michael Hochman, Nicolò Paviato

Let $γ_{n} = O (lo g^{- c} n)$ and let $ν$ be the infinite product measure whose $n$ -th marginal is Bernoulli $(1/2 + γ_{n})$ . We show that $c = 1/2$ is the threshold, above which $ν$ -almo…

math.DS2024

New results on embeddings of self-similar sets via renormalization

Amir Algom, Michael Hochman, Meng Wu

For self-similar sets $X, Y \subseteq R$ , we obtain new results towards the affine embeddings conjecture of Feng-Huang-Rao (2014), and the equivalent weak intersections conj…

math.DS2024

On the dimension of $α β$ -sets

Michael Hochman

We show that the Feng-Xiong lower bound of $1/2$ for the box dimension of $α β$ -sets is tight. We also study how much of an $α β$ -orbit ``carries the dimension'': deleting an arbitar…

math.DS2024

Irreducibility and periodicity in $Z^{2}$ symbolic systems

Michael Hochman

We show that there exist $Z^{2}$ symbolic systems that are strongly irreducible and have no (fully) periodic points

math.DS2023

Some remarks about self-products and entropy

Michael Hochman

Let $(X, B, μ, T)$ be a probability-preserving system with $X$ compact and $T$ a homeomorphism. We show that if every point in $X \times X$ is two-sided recurrent, then $h_μ(…

math.DS2023

On the analytic self-maps of Cantor sets in the line

Michael Hochman

We show that a topological Cantor set in the line has at most countably many real-analytic, onto self-maps.

A threshold for Poisson behavior of non-stationary product measures

New results on embeddings of self-similar sets via renormalization

On the dimension of αβ-sets

Irreducibility and periodicity in Z2 symbolic systems

Some remarks about self-products and entropy

On the analytic self-maps of Cantor sets in the line

On the dimension of $α β$ -sets

Irreducibility and periodicity in $Z^{2}$ symbolic systems