Ariel Rapaport

activity

20232026

most citedDimension of diagonal self-affine sets and measures via non-conformal partitions

1 citations · 1 across the 5 of their papers we have counts for

collaborators

5 papers

math.DS2026

Dimension of self-conformal measures associated to an exponentially separated holomorphic IFS

Zhou Feng, Ariel Rapaport

Let $Φ$ be a holomorphic IFS on a bounded domain in $C$ . Suppose that the following conditions hold: (1) the maps in $Φ$ do not have a common fixed point; (2) there does n…

math.DS2025

Dimension of Furstenberg measures on $CP^{1}$

Ariel Rapaport, Haojie Ren

Let $θ$ be a finitely supported probability measure on $SL (2, C)$ , and suppose that the semigroup generated by $G := supp (θ)$ is strongly irreduci…

math.DS2025

Dimension of self-conformal measures associated to an exponentially separated analytic IFS on $R$

Ariel Rapaport

We extend Hochman's work on exponentially separated self-similar measures on $R$ to the real analytic setting. More precisely, let $Φ = {φ_{i}}_{i \in Λ}$ be an…

math.DS2024

Dimension of Bernoulli Convolutions in $R^{d}$

Ariel Rapaport, Haojie Ren

For $(λ_{1}, ..., λ_{d}) = λ \in (0, 1)^{d}$ with $λ_{1} > ... > λ_{d}$ , denote by $μ_{λ}$ the Bernoulli convolution associated to $λ$ . That is, $μ_{λ}$ is the distribution of the random vector $…

math.DS2023★ 1 cited

Dimension of diagonal self-affine sets and measures via non-conformal partitions

Ariel Rapaport

Let $Φ := {(x_{1}, ..., x_{d}) \to (r_{i, 1} x_{1} + a_{i, 1}, ..., r_{i, d} x_{d} + a_{i, d})}_{i \in Λ}$ be an affine diagonal IFS on $R^{d}$ . Suppose that…

Dimension of self-conformal measures associated to an exponentially separated holomorphic IFS

Dimension of Furstenberg measures on CP1

Dimension of self-conformal measures associated to an exponentially separated analytic IFS on R

Dimension of Bernoulli Convolutions in Rd

Dimension of diagonal self-affine sets and measures via non-conformal partitions

Dimension of Furstenberg measures on $CP^{1}$

Dimension of self-conformal measures associated to an exponentially separated analytic IFS on $R$

Dimension of Bernoulli Convolutions in $R^{d}$