Intersections of polynomial orbits, and a dynamical Mordell-Lang conjecture

Abstract

We prove that if nonlinear complex polynomials of the same degree have orbits with infinite intersection, then the polynomials have a common iterate. We also prove a special case of a conjectured dynamical analogue of the Mordell-Lang conjecture.

19 pages; to appear in Inventiones Mathematicae; in this version we modified the exposition in view of the referee's comments

References in corpus (1)

• A dynamical version of the Mordell-Lang conjecture for the additive group

Cited by in corpus (9)

• Linear relations between polynomial orbits
• A gap principle for dynamics
• A Skolem-Mahler-Lech theorem for iterated automorphisms of $K$-algebras
• The size of quadratic $p$-adic linearization disks
• On the distribution of orbits in affine varieties
• Growth rate of ample heights and the dynamical Mordell-Lang type conjecture
• On the inhomogeneity of the Mandelbrot set
• On intersections of polynomial semigroups orbits with plane lines
• Lower bounds for genera of fiber products