Haojie Ren

activity

20242026

collaborators

4 papers

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 $…

math.CA2024

The high-dimensional Weierstrass functions

Haojie Ren, Weixiao Shen

For a real analytic periodic function $ϕ : R \to R^{d}$ , an integer $b \geq 2$ and $λ \in (1/ b, 1)$ , we prove that the box dimension and the Hausdorff dimension of the grap…

Fourier Decay of SRB Measures for Skew Products

Dimension of Furstenberg measures on CP1

Dimension of Bernoulli Convolutions in Rd

The high-dimensional Weierstrass functions

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

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