5 problems

Let $f$ be a complex cubic map, and let $(A,B)$ be its point in complex parameter space. The connectedness locus consists of maps for which the forward orbits of both critical poin…

Let $s$ be the growth number of the real cubic family, and consider a constant-growth-number locus in the parameter plane. Algebraic-integer conjecture. If this locus has interior…

Let $s(A,b)$ denote the growth number of the real cubic map $x\mapsto x^3-3Ax+b$, and fix a level set $\{(A,b):s(A,b)=s\}$. A map is hyperbolic when its critical orbits converge to…

Consider antipode-preserving cubic maps with parabolic cycles. A parabolic cycle is self-antipodal if it is mapped to itself by the antipodal symmetry, while two parabolic cycles f…

Let ${\bf t}$ be a rotation number, and let ${\pazocal L}_{\bf t}$ denote the compact connected limb associated to ${\bf t}$, with distinguished point ${\boldsymbol\infty}_{\bf t}$…