How to find all Post-Critically Finite Cubic Polynomials with Rational Coefficients
Posted on May 3, 2022
Jackie Anderson, Ph.D.
Bridgewater State University
The orbit of a point P under a function f is the set of iterates ![]()
(P) = {P, f (P), f (f (P)), …}. If this is a finite set, then P is called a preperiodic point for f. If all the critical points of f are preperiodic, we say that f is post-critically finite. For example, the map f (x) = -2×3+3×2 is post-critically finite because both of its critical points (0 and 1) are fixed by f. Post-critically finite maps are rare and have many properties that give them special significance in the study of dynamical systems. In this talk, I will discuss recent work with two collaborators in which we determine the full set of all post-critically finite cubic polynomials with rational coefficients.
Jackie Anderson graduated from Providence College in 2008 and completed her Ph.D. in mathematics at Brown University in 2013. Since then, she has been a faculty member in the mathematics department at Bridgewater State University. Her research interests include number theory, complex and arithmetic dynamics, and voting theory.
