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Finite polynomial orbits. A survey. (English) Zbl 0971.11008
Halter-Koch, Franz (ed.) et al., Algebraic number theory and diophantine analysis. Proceedings of the international conference, Graz, Austria, August 30-September 5, 1998. Berlin: Walter de Gruyter. 331-338 (2000).
A polynomial over a field induces a dynamical system over the closure of that field; in this context, the periodic orbits are objects of primary interest. This short but interesting review, will give the reader an up-to-date account of the main results and questions in this lively area of research, which lies at the interface between algebra and dynamics. The author’s perspective is algebraic.
For the entire collection see [Zbl 0940.00025].

11C08 Polynomials in number theory
12E05 Polynomials in general fields (irreducibility, etc.)
11-02 Research exposition (monographs, survey articles) pertaining to number theory
37B99 Topological dynamics
11R09 Polynomials (irreducibility, etc.)