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Quadratic maps with a periodic critical point of period 2

Canci, Jung Kyu and Vishkautsan, Solomon. (2015) Quadratic maps with a periodic critical point of period 2. Preprints Fachbereich Mathematik, 2015 (39).

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Abstract

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. We provide data related to the analogous classification of graphs of endomorphisms of degree 2 with a rational periodic critical point of period 3 or 4.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Zahlentheorie (Habegger)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Canci, Jung Kyu
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:07 May 2019 15:45
Deposited On:28 Mar 2019 09:52

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