Ariel Rapaport

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

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 $I^¦ = {I ¨ _{i}}_{i \in I^}$ be…

math.DS2024

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

Ariel Rapaport, Haojie Ren

For $(I^»_{1}, ..., I^»_{d}) = I^» \in (0, 1)^{d}$ with $I^»_{1} > ... > I^»_{d}$ , denote by $I^¼_{I^} »$ the Bernoulli convolution associated to $I^»$ . That is, $I^¼_{I^} »$ is the distribution of the rando…

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 Furstenberg measures on $CP^{1}$

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

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