9 problems

Consider the $+-+$ bimodal region and the loci corresponding to constant topological entropy. Plus-minus-plus entropy-disconnection conjecture. In the $+-+$ bimodal region, the cor…

Consider strongly obstructed combinatorics in the bimodal regions of topological shapes $+-+$ and $-+-$, and let $(\Sigma,\Delta)$ denote the moduli coordinates. In the unimodal ca…

Let an admissible combinatorics be given, and consider the successive conjugacy classes generated by the Thurston algorithm. Let the shift locus denote the locus of conjugacy class…

Let $p,p'$ be strictly positive coprime integers, and let ${\rm FP}(p,p')$ denote the conjugacy class in moduli space associated to the Filom–Pilgrim map with these combinatorial p…

Let $\phi$ be a quadratic rational function defined over $\mathbb{Q}$, and let a critical $3$-cycle be the set of iterates of a periodic critical point of period $3$. Period bound…

Let $\phi$ be a quadratic rational function defined over $\mathbb{Q}$ having a $\mathbb{Q}$-rational periodic critical point of period $2$. Period bound conjecture for a rational c…

Let $k$ be the parameter in $K$, set $\phi(x)=k(x^2+1)/x$, and let $\alpha=0$. Let $T_\alpha$ be the rooted tree of preimages of $\alpha$ under iterates of $\phi$, let $G_\infty$ b…

Let $K$ be a number field, let $\phi \in K(z)$ have degree $2$, and let $\alpha \in K$. Let $T_\alpha$ be the rooted tree of preimages of $\alpha$ under iterates of $\phi$, let…

For $n\geq 3$, let $V_n$ be the parameter curve of holomorphic conjugacy classes of quadratic rational maps with a critical point of period $n$, and let $g(V_n)$ denote its geometr…