Linear relations between polynomial orbits

Details Linear relations between polynomial orbits Linear relations between polynomial orbits

2008-07-23

arxiv.org/abs/0807.3576v1

Mathematics

Algebraic Geometry

27 pages

Scientific paper

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.

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