Extra QSeminar: Khazhgali Kozhasov

Speaker: Khazhgali Kozhasov

Title: Rational functions with only real periodic points

Abstract: Any rational function f is known to have infinitely many complex periodic points. Northcott proved that if f is defined over the field of rational numbers, then it has only finitely many rational periodic points. A major open problem in arithmetic dynamics asserts that their number is bounded by a constant depending only on the degree of f. The number of real periodic points of a real rational function f can be finite or infinite (depending on f) and there exist such f whose all periodic points are real. In the talk I will discuss results and questions on the latter (fully-real) situation obtained in a joint work with Mario Kummer.