Simultaneously preperiodic points for families of polynomials in normal form

Dragos Ghioca, Liang Chung Hsia, Khoa Dang Nguyen

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)733-741
Number of pages9
JournalProceedings of the American Mathematical Society
Volume146
Issue number2
DOIs
Publication statusPublished - 2017 Jan 1

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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