Dynamical Belyi maps and arboreal Galois groups

• 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 the geometric Galois groups as subgroups of automorphism groups of regular trees, in terms of iterated wreath products. Using results on the reduction of dynamical Belyi maps modulo certain primes, we obtain results on the corresponding arithmetic Galois groups of iterates. These lead to results on the behavior of the arithmetic Galois groups under specialization, with applications to dynamical sequences.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Primary: 11G32

12F10

Secondary: 37P05

37P15

Publication and Content Type

ref (subject category)

art (subject category)