J. K. Canci, Solomon Vishkautsan
Published 2015-10-15Version 1
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.
Some families of polynomials satisfying uniform boundedness for rational preperiodic points
Explicit Descriptions of Quadratic Maps on $\pp^1$ defined over a field $K$
Determination of all rational preperiodic points for morphisms of PN
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