We study the orbits of a polynomial , namely, the sets with . We prove that if two nonlinear complex polynomials have orbits with infinite intersection, then and have a common iterate. More generally, we describe the intersection of any line in with a -tuple of orbits of nonlinear polynomials, and we formulate a question which generalizes both this result and the Mordell–Lang conjecture.
Dragos Ghioca. Thomas J. Tucker. Michael E. Zieve. "Linear relations between polynomial orbits." Duke Math. J. 161 (7) 1379 - 1410, 15 May 2012. https://doi.org/10.1215/00127094-1598098