On algebraic integers of bounded house and preperiodicity in polynomial semigroup dynamics
HTML articles powered by AMS MathViewer
- by Alina Ostafe and Marley Young PDF
- Trans. Amer. Math. Soc. 373 (2020), 2191-2206 Request permission
Abstract:
We consider semigroup dynamical systems defined by several polynomials over a number field $\mathbb {K}$, and the orbit (tree) they generate at a given point. We obtain finiteness results for the set of preperiodic points of such systems that fall in the cyclotomic closure of $\mathbb {K}$. More generally, we consider the finiteness of initial points in the cyclotomic closure for which the orbit contains an algebraic integer of bounded house. This work extends previous results for classical obits generated by one polynomial over $\mathbb {K}$ obtained initially by Dvornicich and Zannier (for preperiodic points), and then by Chen and Ostafe (for roots of unity and elements of bounded house in orbits).References
Additional Information
- Alina Ostafe
- Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales 2052, Australia
- MR Author ID: 884181
- Email: alina.ostafe@unsw.edu.au
- Marley Young
- Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales 2052, Australia
- Email: marley.young@unsw.edu.au
- Received by editor(s): February 14, 2019
- Received by editor(s) in revised form: August 12, 2019, and August 13, 2019
- Published electronically: October 1, 2019
- Additional Notes: This work was supported in part by the Australian Research Council Grant DP180100201.
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 2191-2206
- MSC (2010): Primary 11R18, 37F10
- DOI: https://doi.org/10.1090/tran/7974
- MathSciNet review: 4068295