Powers in Orbits of Rational Functions: Cases of an Arithmetic Dynamical Mordell–Lang Conjecture

Let $K$ be a finitely generated field of characteristic zero. For fixed $m\geqslant 2$ , we study the rational functions $\unicode[STIX]{x1D719}$ defined over $K$ that have a $K$ -orbit containing infinitely many distinct $m$ -th powers. For $m\geqslant 5$ we show that the only such functions are th...

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Bibliographic Details

Published in:	Canadian journal of mathematics Vol. 71; no. 4; pp. 773 - 817
Main Authors:	Cahn, Jordan, Jones, Rafe, Spear, Jacob
Format:	Journal Article
Language:	English
Published:	Canada Canadian Mathematical Society 01.08.2019 Cambridge University Press
Subjects:	Mathematics Numbers Lattès map iteration of rational functions 11G05 37P15 37P05 genus of variables-separated curve arithmetic dynamics special orbits of rational function
ISSN:	0008-414X, 1496-4279
Online Access:	Get full text
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