ﻻ يوجد ملخص باللغة العربية
We study the dynamical properties of a large class of rational maps with exactly three ramification points. By constructing families of such maps, we obtain infinitely many conservative maps of degree $d$; this answers a question of Silverman. Rather precise results on the reduction of these maps yield strong information on the rational dynamics.
We consider a large class of so-called dynamical Belyi maps and study the Galois groups of iterates of such maps. From the combinatorial invariants of the maps, we construct a useful presentation of their Galois groups as subgroups of automorphism gr
Riemanns Existence Theorem gives the following bijections: (1) Isomorphism classes of Belyi maps of degree $d$. (2) Equivalence classes of generating systems of degree $d$. (3) Isomorphism classes of dessins denfants with $d$ edges. In previous work,
We give necessary and sufficient conditions for post-critically finite polynomials to have potential good reduction at a given prime. We also answer in the negative a question posed by Silverman about conservative polynomials. Both proofs rely on dyn
We prove existence and nonexistence results for certain differential forms in positive characteristic, called {em good deformation data}. Some of these results are obtained by reduction modulo $p$ of Belyi maps. As an application, we solve the local
The dynamical degree of a dominant rational map $f:mathbb{P}^Nrightarrowmathbb{P}^N$ is the quantity $delta(f):=lim(text{deg} f^n)^{1/n}$. We study the variation of dynamical degrees in 1-parameter families of maps $f_T$. We make a conjecture and ask