Linear relations between polynomial orbits

By Dragos Ghioca, T. Tucker, Michael E. Zieve. 2008

60 citations recorded by the source corpus.

We study the orbits of a polynomial f 2CŒX , namely, the sets 1 ;f . /; f .f . //; : : :o with 2 C. We prove that if two nonlinear complex polynomials f;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 with a d -tuple of orbits of nonlinear polynomials, and we formulate a question which generalizes both this result and the Mordell–Lang conjecture.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c404ffb8ade5542d78f319a11c13670ad9b4c2b8

Citations in the corpus

• Dynamics on Berkovich Spaces in Low Dimensions (2012, unknown): “er the complex numbers. We shall see some instances of this phenomenon in these notes; other examples are provided by the work of Kiwi [Kiw06], Baker and DeMarco [BdM09], and Ghioca, Tucker and Zieve [GTZ08]. Over the complex numbers, many of the most powerful tools for studying dynamics are either ”