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A dynamical Mordell-Lang property on the disk


Author: Ming-Xi Wang
Journal: Trans. Amer. Math. Soc. 369 (2017), 2183-2204
MSC (2010): Primary 11Z05; Secondary 37P05
DOI: https://doi.org/10.1090/tran/6775
Published electronically: October 31, 2016
MathSciNet review: 3581231
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Abstract: We prove that two finite endomorphisms of the unit disk with degree at least two have orbits with infinite intersections if and only if they have a common iterate.


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Additional Information

Ming-Xi Wang
Affiliation: Department of Mathematics, University of Salzburg, Hellbrunnerstr. 34/I, 5020 Salzburg, Austria
Email: mingxi.waeng@gmail.com

DOI: https://doi.org/10.1090/tran/6775
Keywords: Arithmetic dynamics, fundamental group, rational points, Blaschke product, Faltings' theorem, heights, monodromy, elliptic rational function.
Received by editor(s): December 20, 2013
Received by editor(s) in revised form: April 12, 2015, and June 16, 2015
Published electronically: October 31, 2016
Additional Notes: The author was partially supported by a scholarship of ZGSM and the SNF grant and Austrian Science Fund(FWF): P24574.
Article copyright: © Copyright 2016 American Mathematical Society