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Zbl 0860.11065
Morton, Patrick
On certain algebraic curves related to polynomial maps. (English)
[J] Compos. Math. 103, No.3, 319-350 (1996). ISSN 0010-437X; ISSN 1570-5846/e

This is an interesting and well-written paper, exploring the interface between meromorphic dynamics and Galois theory. The author introduces algebraic methods to deal with questions of irreducibility of certain polynomials, which had been previously approached only using dynamics. The main result is that there is only a finite number of cyclic extensions of a field, whose Galois group is generated by a given polynomial dynamical system.
[Franco Vivaldi (London)]

MSC 2000:: *11R09 Polynomials over global fields
37P05
12F12 Inverse Galois theory

Keywords: irreducibility of polynomials; algebraic dynamics; meromorphic dynamics; Galois theory; Galois group; polynomial dynamical system

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