Mathematics

Let f:X -> X be a morphism of varieties over a field of characteristic 0 and let x be a point on X.  In many cases, one can show the orbit of x under f can be "p-adically parametrized"; that is, one can find a p-adic analytic map g from a disc in C_p to X such that g(n) = f^n(x) for all n.  The existence of such a parametrization allows one to solve the so-called ``dynamical Mordell-Lang problem'' for f, which states that, given a subvariety W of X, the set of n such that f^n(x) is in W forms a finite union of arithmetic sequences.  It also allows for the solution of various weak forms of a conjecture of Zhang on the existence of points with Zariski dense orbits.