During work on the article “Scarcity of cycles for rational functions over a number field”, Jung Kyu Canci and I proved as a corollary that a rational function defined over with everywhere good reduction has at most periodic points. As a special case, we remarked that a monic polynomial with integer coefficients has at most -rational periodic points. It turns out that much better can be said, and that G. Baron proved in 1991 in an unpublished paper that such a polynomial has at most periodic points, including the point at infinity. I decided to translate the article from the original German, and bring it the mathematical community’s attention. I marked in red additions made by me. Any mistakes are probably due to my translation.

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# Arithmetic dynamics

# Bibliography of arithmetic dynamics of quadratic rational maps

Here is a list of articles that relate to the dynamics of quadratic rational maps. Some are not arithmetic in nature, but are important for arithmetic considerations as well. Let me know if there are of articles on this topic you think should be in the list.

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