Dynamics of functions arising from Pisot and Salem polynomials

Somjate Chaiya, Aimo Hinkkanen

Research output: Contribution to journalArticlepeer-review

Abstract

Let Q(z) = znP(z) − zdeg PP(z−1), where P is the minimal polynomial of a Pisot number. Boyd [Duke Math. J. 44 (1977), 315–328] showed that, for (Formula presented.), Q is the product of cyclotomic polynomials and the minimal polynomial of a Salem number, say α. In this paper, we study the dynamics of the Newton map N = z − Q/Q′ induced by Q in the immediate basin Uα of α. We establish that N is a 2-fold covering map of Uα onto itself. Furthermore, there exists a conformal mapping φ of Uα onto the open unit disk D such that (Formula presented.) for all z∈D.

Original languageEnglish (US)
Pages (from-to)371-378
Number of pages8
JournalJournal of Fixed Point Theory and Applications
Volume17
Issue number2
DOIs
StatePublished - Jun 23 2015

Keywords

  • Primary 37F10
  • Secondary 11R06

ASJC Scopus subject areas

  • Modeling and Simulation
  • Geometry and Topology
  • Applied Mathematics

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