Let $\{f_i(x)=M_ix+a_i\}_{i\in I}$ be an affine iterated function system on $\mathbb{R}^d$ with attractor $\Lambda$, and let $\mu$ be an associated self-affine measure. Assume that the $M_i$ generate a Zariski dense subgroup of $\mathrm{GL}_d(\mathbb{R})$. Under the strong open set condition, we show that $\dim_{\mathr...
We establish that for a $C^r$-generic surface repeller ($1<r \leq \infty$), its Hausdorff and box dimensions are exactly the unique zero of the sub-additive topological pressure function. As an application of our framework, we show that the attractor of a uniformly non-conformal and weakly irreducible planar non-linear...
Jialun Li, Wen-Yu Pan, Yao Tong et al.· 3 citations· ⚡2
Let $\Gamma<\operatorname{PSL}_2(\mathbb R)$ be a torsion-free, non-elementary, finitely generated Fuchsian group with parabolic elements, and let $\rho:\Gamma\to G$ be a type-preserving, Zariski dense, positive representation into a connected split semisimple real algebraic group. We prove quantitative local mixing fo...
Dongryul M. Kim, Hee Oh, Wen-Yu Pan· 0 citations
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