Simultaneously preperiodic points for families of polynomials in normal form
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- by Dragos Ghioca, Liang-Chung Hsia and Khoa Dang Nguyen PDF
- Proc. Amer. Math. Soc. 146 (2018), 733-741 Request permission
Abstract:
Let $d>m>1$ be integers, let $c_1,\dots , c_{m+1}$ be distinct complex numbers, and let $\mathbf {f}(z):=z^d+t_1z^{m-1}+t_2z^{m-2}+\cdots + t_{m-1}z+t_m$ be an $m$-parameter family of polynomials. We prove that the set of $m$-tuples of parameters $(t_1,\dots , t_m)\in \mathbb {C}^m$ with the property that each $c_i$ (for $i=1,\dots , m+1$) is preperiodic under the action of the corresponding polynomial $\mathbf {f}(z)$ is contained in finitely many hypersurfaces of the parameter space $\mathbb {A}^m$.References
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Additional Information
- Dragos Ghioca
- Affiliation: Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
- MR Author ID: 776484
- Email: dghioca@math.ubc.ca
- Liang-Chung Hsia
- Affiliation: Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, ROC
- MR Author ID: 606569
- Email: hsia@math.ntnu.edu.tw
- Khoa Dang Nguyen
- Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 4T4, Canada
- MR Author ID: 886774
- Email: dangkhoa.nguyen@ucalgary.ca
- Received by editor(s): November 6, 2016
- Received by editor(s) in revised form: April 5, 2017
- Published electronically: September 7, 2017
- Additional Notes: The research of the first author was partially supported by an NSERC Discovery grant.
The second author was supported by MOST grant 105-2918-I-003-006.
The third author was partially supported by a UBC-PIMS fellowship - Communicated by: Matthew A. Papanikolas
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 733-741
- MSC (2010): Primary 37P05; Secondary 37P30, 37P45
- DOI: https://doi.org/10.1090/proc/13762
- MathSciNet review: 3731706