Papers › Dynatomic Galois groups for a family of quadratic rational maps
Dynatomic Galois groups for a family of quadratic rational maps
David Krumm, Allan Lacy
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For every nonconstant rational function ϕ∈ℚ(x), the Galois groups of the dynatomic polynomials of ϕ encode various properties of ϕ that are of interest in the subject of arithmetic dynamics. We study here the structure of these Galois groups as ϕ varies in a particular one-parameter family of maps, namely the quadratic rational maps having a critical point of period 2. In particular, we provide explicit descriptions of the third and fourth dynatomic Galois groups for maps in this family.
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