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

By Dragos Ghioca, T. Tucker, Michael E. Zieve. 2007

95 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/48baf2cc043c0df480d1cbf824944dde004e2df2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Joseph H. Silverman
2. T. Tucker
3. Dragos Ghioca
4. Robert L. Benedetto
5. Pär Kurlberg
6. Matthew Baker
7. Samir Siksek
8. Sergei V. Kozyrev

In Discrete Mathematics and Combinatorics

1. Joseph H. Silverman
2. T. Tucker
3. Dragos Ghioca
4. Robert L. Benedetto
5. Pär Kurlberg

In Geometry and Topology

1. Robert L. Benedetto
2. T. Tucker
3. Pär Kurlberg
4. Joseph H. Silverman
5. Dragos Ghioca
6. Laura Demarco
7. Matthew Baker
8. Shu Kawaguchi

Citations in the corpus

• Periods of rational maps modulo primes (2011, unknown): “The following conjecture was proposed in [8,10].”
• A case of the dynamical Mordell–Lang conjecture (2012, background): “In the cyclic case, however, the results of the present paper are somewhat more general, because our techniques allow the subvariety V to be an arbitrary curve, rather than a line as in [14] and [16].”
• Dynamical Degrees, Arithmetic Degrees, and Canonical Heights for Dominant Rational Self-Maps of Projective Space (2011, background): “But some carefully formulated dynamical Manin–Mumford statements have been proven; see for example [28, 29].”