TY - JOUR

T1 - Simultaneously preperiodic points for families of polynomials in normal form

AU - Ghioca, Dragos

AU - Hsia, Liang Chung

AU - Nguyen, Khoa Dang

N1 - Funding Information:
Received by the editors November 6, 2016 and, in revised form, April 5, 2017. 2010 Mathematics Subject Classification. Primary 37P05; Secondary 37P30, 37P45. 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.

PY - 2017

Y1 - 2017

N2 - Let d > m > 1 be integers, let c1, …, cm+1 be distinct complex numbers, and let f(z):= zd + t1 zm−1 + t2 zm−2 + · · · + tm−1 z + tm be an m-parameter family of polynomials. We prove that the set of m-tuples of parameters (t1, …, tm) ∈ Cm with the property that each ci (for i = 1, …, m+1) is preperiodic under the action of the corresponding polynomial f(z) is contained in finitely many hypersurfaces of the parameter space Am.

AB - Let d > m > 1 be integers, let c1, …, cm+1 be distinct complex numbers, and let f(z):= zd + t1 zm−1 + t2 zm−2 + · · · + tm−1 z + tm be an m-parameter family of polynomials. We prove that the set of m-tuples of parameters (t1, …, tm) ∈ Cm with the property that each ci (for i = 1, …, m+1) is preperiodic under the action of the corresponding polynomial f(z) is contained in finitely many hypersurfaces of the parameter space Am.

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U2 - 10.1090/proc/13762

DO - 10.1090/proc/13762

M3 - Article

AN - SCOPUS:85037598492

VL - 146

SP - 733

EP - 741

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -