Seminar Algebra and Geometry: Jung-Kyu Canci (Basel)

Quadratic maps with a periodic critical point of period 2

In a recent work in collaboration with Salomon Vishkautasan, we provide a complete classification of possible graphs of rational preperiodic points of endomorphisms of the projective line of degree 2 defined over the rationals with a rational periodic critical point of period 2, under the assumption that these maps have no periodic points of period at least 5. We explain how this extends results of Poonen on quadratic polynomials. We show that there are 13 possible graphs, and that such maps have at most 9 rational preperiodic points.

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