4 problems

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 $\phi$ 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…