Linear relations between polynomial orbits
Algebraic Geometry
2019-12-19 v1 Dynamical Systems
Abstract
We study the orbits of a polynomial f in C[X], namely the sets {e,f(e),f(f(e)),...} with e in C. We prove that if nonlinear complex polynomials f and g have orbits with infinite intersection, then f and g have a common iterate. More generally, we describe the intersection of any line in C^d with a d-tuple of orbits of nonlinear polynomials, and we formulate a question which generalizes both this result and the Mordell--Lang conjecture.
Cite
@article{arxiv.0807.3576,
title = {Linear relations between polynomial orbits},
author = {Dragos Ghioca and Thomas J. Tucker and Michael E. Zieve},
journal= {arXiv preprint arXiv:0807.3576},
year = {2019}
}
Comments
27 pages