Event Detail

Event Type: 
Number Theory Seminar
Tuesday, May 17, 2016 - 16:00 to 17:00
StAg 263

Morton and Silverman proved that, for any rational map with rational coefficients of degree at least 2 such that the second iterate is not a polynomial, the forward orbit of any rational number contains only finitely many integers. This finiteness condition is false for polynomials, but not every polynomial with rational coefficients contains an orbit with infinitely many integers. Using a classification of p-adic filled Julia sets of quadratic polynomials, due to Benedetto, Briend, and Perdry, we provide necessary and sufficient conditions for a quadratic polynomial of potentially good reduction to have an infinite integer orbit. Necessary background in arithmetic dynamics and p-adic numbers will be provided.