### 12 juli 2007, kl 13.15-14.15, KTH, sal 3721.

### Thomas J. Tucker (Rochester University):
Intersections of polynomial orbits, and a dynamical
Mordell-Lang conjecture

**Abstract.**
We prove that if two nonlinear complex polynomials of the
same degree have orbits with infinite intersection, then the
polynomials have a common iterate. This naturally gives rise to a
special case of a dynamical analogue of the Mordell-Lang conjecture,
one that holds for lines in the affine plane A^1 x A^1, under the
action of polynomials acting on each coordinate. The proof uses
classical results of Ritt for polynomials along with a result of Bilu
and Tichy on integral points to establish the result over number
fields. The general case over C is then obtained by a specialization
argument.