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We study the orbits of a polynomial $f\in \mathbb {C}[X]$ , namely, the sets $\{\alpha,f(\alpha),f(f(\alpha)),\ldots\}$ with $\alpha\in \mathbb {C}$ . 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 $\mathbb {C}^{d}$ 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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Autor(es)

Ghioca, Dragos -  Tucker, Thomas J. -  Zieve, Michael E. - 

Id.: 55259223

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras clave37F10 - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2012 Duke University Press

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 0012-7094
[References] 1547-7398

Fecha de contribución: 25-jul-2012

Contacto:

Localización:
* Duke Math. J. 161, no. 7 (2012), 1379-1410
* doi:10.1215/00127094-1598098

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