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

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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.

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Authors and Affiliations

  1. Department of Mathematics & Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, AB, T1K 3M4, Canada

    Dragos Ghioca

  2. Department of Mathematics, University of Rochester, Hylan Building, Rochester, NY, 14627, USA

    Thomas J. Tucker

  3. Center for Communications Research, 805 Bunn Drive, Princeton, NJ, 08540, USA

    Michael E. Zieve

Authors
  1. Dragos Ghioca
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  2. Thomas J. Tucker
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  3. Michael E. Zieve
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Corresponding author

Correspondence to Dragos Ghioca.

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Mathematics Subject Classification (1991)

Primary 14G25; Secondary 37F10, 11C08

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Ghioca, D., Tucker, T. & Zieve, M. Intersections of polynomial orbits, and a dynamical Mordell–Lang conjecture. Invent. math. 171, 463–483 (2008). https://doi.org/10.1007/s00222-007-0087-5

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  • DOI: https://doi.org/10.1007/s00222-007-0087-5

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