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15 May 2012 Linear relations between polynomial orbits
Dragos Ghioca, Thomas J. Tucker, Michael E. Zieve
Duke Math. J. 161(7): 1379-1410 (15 May 2012). DOI: 10.1215/00127094-1598098

Abstract

We study the orbits of a polynomial fC[X], namely, the sets {α,f(α),f(f(α)),} with αC. 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 Cd 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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Dragos Ghioca. Thomas J. Tucker. Michael E. Zieve. "Linear relations between polynomial orbits." Duke Math. J. 161 (7) 1379 - 1410, 15 May 2012. https://doi.org/10.1215/00127094-1598098

Information

Published: 15 May 2012
First available in Project Euclid: 4 May 2012

zbMATH: 1267.37043
MathSciNet: MR2922378
Digital Object Identifier: 10.1215/00127094-1598098

Subjects:
Primary: 37F10
Secondary: 11C08, 14G99

Rights: Copyright © 2012 Duke University Press

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Vol.161 • No. 7 • 15 May 2012
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