ﻻ يوجد ملخص باللغة العربية
Let $f:{mathbb P}^nto{mathbb P}^n$ be a morphism of degree $dge2$. The map $f$ is said to be post-critically finite (PCF) if there exist integers $kge1$ and $ellge0$ such that the critical locus $operatorname{Crit}_f$ satisfies $f^{k+ell}(operatorname{Crit}_f)subseteq{f^ell(operatorname{Crit}_f)}$. The smallest such $ell$ is called the tail-length. We prove that for $dge3$ and $nge2$, the set of PCF maps $f$ with tail-length at most $2$ is not Zariski dense in the the parameter space of all such maps. In particular, maps with periodic critical loci, i.e., with $ell=0$, are not Zariski dense.
A rational function of degree at least two with coefficients in an algebraically closed field is post-critically finite (PCF) if all of its critical points have finite forward orbit under iteration. We show that the collection of PCF rational functio
We describe and implement an algorithm to find all post-critically finite (PCF) cubic polynomials defined over $mathbb{Q}$, up to conjugacy over $text{PGL}_2(bar{mathbb{Q}})$. We describe normal forms that classify equivalence classes of cubic polyno
We compare different notions of limit sets for the action of Kleinian groups on the $n-$dimensional projective space via the irreducible representation $varrho:PSL(2,mathbb{C})to PSL(n+1,mathbb{C}).$ In particular, we prove that if the Kleinian group
Motivated by the dynamical uniform boundedness conjecture of Morton and Silverman, specifically in the case of quadratic polynomials, we give a formal construction of a certain class of dynamical analogues of classical modular curves. The preperiodic
We propose a new theory of (non-split) P^n-functors. These are F: A -> B for which the adjunction monad RF is a repeated extension of Id_A by powers of an autoequivalence H and three conditions are satisfied: the monad condition, the adjoints conditi