4 problems

Let $\mathcal{T}$ be the parameter triangle for the family of beta-transformations, with parameters $(\alpha,\beta)$. A beta-transformation is topologically LEO when it has the loc…

Let $\mathcal{T}$ be the parameter triangle for the family of beta-transformations, with parameters $(\alpha,\beta)$. Transitivity conjecture. For all parameters in $\mathcal{T}$ s…

Let $\beta\in(1,2]$. The bifurcation-set equality conjecture. … if and only if $\mathcal{E}_\beta$ has no isolated points. Here $\mathcal{E}_\beta$ is the set-valued bifurcation se…

Let $\beta$ be a Pisot number, meaning an algebraic integer greater than $1$ whose other Galois conjugates have modulus less than $1$, and let $A_\beta$ denote the associated attra…