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This article is a survey of two subjects: the first part is devoted to fieldgenerators in two variables, and the second to birational endomorphisms of theaffine plane. Each one of these subjects originated in Abhyankar's seminar inPurdue University in the 1970s. Note that the part on field generators is morethan a survey, since it contains a considerable amount of new material.

Field generators in two variables and birational endomorphisms of $\mathbb{A}^2$