7 problems

Let $E,F\subset\mathbb{R}^d$ be two totally disconnected non-trivial self-similar sets, generated by iterated function systems $\Phi=\{\varphi_i\}_{i\in I}$ and…

Popov–Pommerening conjecture. Any observable regular subgroup of $G$ is a Grosshans subgroup.

Let $F$ and $E$ be self-similar sets, and suppose that $F$ embeds into $E$ by an affine map. Feng–Huang–Rao's algebraic-dependence conjecture. Every contraction ratio of $F$ should…

Feng–Huang–Rao's conjecture. If, for some $i\in I$, $\log\alpha_i\notin\operatorname{span}_{\mathbb{Q}}\\{\log\beta_j\\}_{j\in J}$, then

Let $\Phi=\{\phi_i(x)=\alpha_i x+a_i\}_{i=1}^m$ and $\Psi=\{\psi_j(x)=\beta_jx+b_j\}_{j=1}^{\ell}$ be self-similar iterated function systems on $\mathbb R$, with attractors…

Let $A_\lambda$ denote a self-similar set arising from a homogeneous iterated function system with contraction ratio $\lambda$, satisfying the open set condition and having dimensi…

Feng's logarithmic commensurability conjecture. For every $1\leq i\leq l$, there exist $t_{i,j}\in\mathbb{Q}$ with $t_{i,j}\geq0$ such that