Periodic points, linearizing maps, and the dynamical Mordell-Lang   problem
  We prove a dynamical version of the Mordell-Lang conjecture for subvarieties of quasiprojective varieties X, endowed with the action of a morphism f:X --> X. We use an analytic method based on the technique of Skolem, Mahler, and Lech, along with results of Herman and Yoccoz from nonarchimedean dynamics. 
Dragos Ghioca and Thomas J. Tucker