Haojie Ren

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20242026

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math.DS2026

Fourier Decay of SRB Measures for Skew Products

Gaétan Leclerc, Haojie Ren

We study Fourier decay of natural invariant measures for real analytic skew products $T (x, y) = (f (x), g (x, y))$ on $S^{1} \times [- 1, 1]$ , where $f$ is expanding and $0<|\partial…

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.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 $…

Fourier Decay of SRB Measures for Skew Products

Dimension of Furstenberg measures on CP1

Dimension of Bernoulli Convolutions in Rd

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

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