Integer points in orbits on P^1

Let f be a rational map on P^1 defined over the rationals Q whose second iterate f^2 is not a polynomial. For x in Q, Silverman has shown that there are only finitely many integers in the forward orbit {x,f(x),…,f^n(x),…}. In this talk, we present results about the more general setting of S-integers in orbits, where S is a finite set of primes, and provide new upper bounds on the number of S-integers in orbits in terms of the size |S|.

Please see http://people.math.harvard.edu/~demarco/AlgebraicDynamics/ for more information