Orbits of Algebraic Dynamical Systems in Subgroups and Subfields

Chapter

Abstract

We study intersections of orbits in polynomial dynamics with multiplicative subgroups and subfields of arbitrary fields of characteristic zero, as well as with sets of points that are close with respect to the Weil height to division groups of finitely generated groups of \(\overline{\mathbb{Q}}^{{\ast}}\).

2010 Mathematics Subject Classification

Primary 37P05 Secondary 11G25 11G35 13P15 37P25 

Notes

Acknowledgements

The authors are grateful to Umberto Zannier for several valuable suggestions, in particular the idea of the proof of Theorem 2.1 appeared from one of these suggestions. The authors would also like to thank Michael Zieve for patient explanation of several issues related to the material of Sect. 3.2 and in particular for outlining the argument about orbits in subfields of number fields.

During the preparation of this paper, A. Ostafe was partially supported by the UNSW Vice Chancellor’s Fellowship and I.E. Shparlinski by the Australian Research Council Grant DP140100118.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of New South WalesSydneyAustralia

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